Magnetically Floating Landmasses
Your world seems to be a bit bigger than the Earth (7,900km radius vs 6,371km radius). This could possibly cause the planet to have a higher gravitational pull, meaning your electromagnetic fields holding these floating landmasses in the air might have to be even stronger than first imagined. But even if your world was the same size as the Earth you would still have problems.
Electromagnetic fields can affect human physiology. Consider that neurons in the brain send electrical impulses, and under a sufficiently strong enough electromagnetic field this could be effected or even negated altogether. International guidelines for public exposure to magnetic fields set an upper limit of 40 millitesla – around 1,000 times stronger than the Earth’s magnetic field.
Milliteslas are a unit of magnetic flux density. Magnetic fields go down as the cube of the distance increases - meaning that their strength dissipates quickly across even short distances.
You're talking about a magnetic field strong enough to suspend landmasses weighing at least billions of tonnes a minimum of 5km in the air. Not only 5km, but also some approaching 19km up in the air. This would require a magnetic field that is exponentially bigger than our guidelines for exposure.
In short, the magnetic field would be so strong that it would render any life on the planet dead from intense EM radiation.
Weather
In terms of weather, we first have to consider the atmosphere. Atmospheres are not consistent. The closer to the planet you get, the thicker the atmosphere.
Here is a graph of elevation vs air pressure here on Earth:

As you can see, at sea level we have air pressure of 100kPa, however 5km up we have almost half that air pressure (around 55kPa). On your mid layer, around 14km high, we have atmospheric pressure that is less than 20kPa.
Atmospheric pressure decreases as the height of a surface above ground level increases. This is because, as the altitude increases:
- the number of air molecules decreases
- the weight of the air decreases
- there is less air above a surface
This is why aircraft that fly at high altitudes must be pressurised. If the air pressure is too low, humans cannot take in oxygen quickly enough to meet their bodies’ needs.
It is the lack of oxygen rather than the reduced air pressure that actually limits the height at which we can breathe. An elevation of about 6km above sea level is the maximum height at which sufficient oxygen exists in the air to sustain us. People would find it difficult to breathe properly on the first layer of floating landmasses, and they wouldn't be able to breathe at all on any of the higher layers.
This also means the impact of these landmasses on the weather would lessen considerably the higher you went up. The first layer would probably have the most impact, I could see them acting like inverse mountains, forcing the air to become more dense underneath the landmasses and probably encouraging cloud formations. It is quite possible the first layer of land masses would appear to be floating on clouds due to this phenomenon.
Higher up layers would have an impact on the weather, only much less so as there is significantly less air the higher you go up. Even 5km is quite high up. But I have other concerns about these higher up layers.
Wind Speed
In terms of wind speeds, first consider that the Earth is rotating at about 1,000mph, and yet most wind speeds are around 3-30mph, with only something like hurricanes or cyclones witnessing wind speeds in excess of 70mph. In essence, the air is more or less moving with the rotation of the Earth.
As a result I don't think the wind speed would change much from your first layer of floating landmasses, as the planet and this layer are both moving in the same direction, albeit at slightly different speeds.
Where it gets interesting is when you have the higher up layers moving in the opposite direction. Although there is less air pressure up there, you are talking about huge landmasses moving at around 1,000m/s relative to the surface.
This is almost 3 times the speed of sound (Mach 2.9 to be precise). This is the speed of artillery cannons, tank cannons and sniper rifles. There are some jet aeroplanes that exceed this speed. Commerical passenger planes are usually doing 250m/s.
So we have a floating landmass the size of Africa moving at almost Mach 3. I'm imagining the upper atmosphere to resemble something like this:

This is a shot from the film Independance Day. This is a huge spaceship entering the atmosphere from space. I believe these spaceships were only about 15 miles in diameter, compare that to the size of the UK or Africa. The burning clouds are fairly accurate considering the heat and friction of entering the Earths atmosphere from space - most things entering the atmosphere from the cold of space will "burn up".
Your landmasses are not entering from space or changing in temperature much - however they are significantly bigger and moving at supersonic speeds. Aerodynamic heating is the heating of a solid body produced by its high-speed passage through air, whereby its kinetic energy is converted to heat by adiabatic heating. You're going to get a lot of this.
I can imagine the air friction and adiabatic heating to be enough to generate incredible heat and probably fire, even at those heights and air pressures. Your mid and upper layers are going to be surrounded by a burning cloud of fire the entire time they are moving at these speeds. It is very likely that you'd never actually see the floating landmass inside these burning clouds of fire.
For the purposes of this thought experiment, I am going to ignore the fact that these perpetually burning clouds would, sooner or later, ignite the atmosphere of the entire world, thus depleting it of all oxygen.
Light & Sound
And we're not even mentioning the noise this would make - if you've ever heard a jet plane fly overhead at supersonic speeds, just consider for a moment that noise is being created by a mere plane travelling at that speed. Something the size of Africa travelling at that speed, constantly, would create a deafening wall of unending noise.
The constantly burning cloud being caused by a floating landmass the size of Africa rushing over the surface of the world at Mach 3 would be far bigger than the landmass itself. This isn't even counting the burning friction clouds from the upper layer. Then the lower layer of floating landmasses would block even more light that made it down this far.
Even if we ignore all the burning clouds - a continent the size of Africa is thousands of miles in any direction, for the purposes of this I'm going to assume 4,600 miles. Even when moving at Mach 3, it'll take about 85 days (assuming a 24 hour day) for just one of these floating landmasses to pass over a single spot on the surface. That's nearly 3 months of continuous pitch-black shadow just from one of these huge floating landmasses.
During this time the entire sky would be filled, horizon to horizon, with the overhead landmass. This 85 day period is just the amount of time the landmass would be directly overhead, it does not count the shadows caused by the landmass as it's approaching or leaving over the horizon. And that's just one of these landmasses, I am guessing you have more?
Let's just say that light would rarely ever reach the surface of the world.
Supporting Life
As mentioned, the whole world is uninhabitable due to intense EM radiation, but lets suppose we ignore that for a second.
The mid and upper layers would be uninhabitable, and not only because of their speed & the burning friction cloud, but also because they are far too high up in the atmosphere and there wouldn't be enough air to support life.
Even on the lower level, 5km up is about 200 meters above the tree line, so you might get some basic moulds and algaes living on this level but even this is highly unlikely. Bacteria could possibly survive, maybe.
On the surface? Very little light would reach this part of the world, so again, maybe moulds and bacteria. And just to put it into context, it would be very unlikely any life of any kind would survive on this world:
You've created a hellscape of shadows, burning clouds, endless deafening noise and the kinds of intense EM radiation that is usually only associated with Pulsars or Black Holes.
This is not a habitable world.
Conclusion
If you want this world, ignore science.
Say it all works because "magic".
It's the only way you'll get your world, as is, to be able to support anything more than some bacteria.
If you want to be science based, you are going to have to change a lot of things if you want your world capable of supporting an atmosphere (and therefore weather), let alone any kind of life.
The vertical spread of your floating landmasses is causing you issues. You'll want your layers lower down, and you'll want as few layers as possible. The size of the landmasses will need to be significantly reduced (UK would want to be your absolute largest size, and only then if it had holes/gaps in it to let light through) - and you definitely don't want any of these landmasses travelling faster than 343m/s (the speed of sound) relative to the surface of your planet, preferably much, much slower (maybe 50-200m/s, with lower speeds for the bigger landmasses to minimise air displacement).
Simply put, the scale of everything you are talking about is way too big, way too fast and way too high.
If you want something along the lines of "the floating mountains of Pandora" from the film Avatar, then these have trees growing on them, meaning these floating mountains are lower than the treeline (about 4,800m up).

In general, 5km up is pretty high up. Even if you increase the amount of oxygen available at these altitudes, you're going to run into problems. Consider that Mount Everest itself is 8.8km up, which isn't far above the uppermost height of your first layer. My guess is that you want life of some sort, perhaps even civilizations living on these floating landmasses. If that's the case, they need to be much further down in altitude.
Historically, people settled in valleys, not hilltops, simply because it was warmer and less windy - less exposed. Human life atop a floating landmass would be difficult at best. Human life atop the floating landmasses you've described would be a death sentence, even without the radiation or noise or burning clouds. It would just be too cold and exposed. Mountain tops at the equator are covered in ice and snow all year round so long as they are about 4.5km high. Your floating landmasses would be more akin to Antartica than Africa.
And if you really want to be science based, don't have these layers of floating landmass hovering because of an electromagnetic field. It sounds reasonable enough to the layman, hence why it's used in Avatar. But in reality, to get even a single mountain floating a short distance above the ground would require an electromagetic field that would be, at the very least, harmful to all biological life.
Ancient technology of a long lost civilization or something similar could give you what you want but without all the intense radiation. Have them put anti-gravity devices into continents or something similar to produce the effect you want.
If you wanted these layers to only last a few years at most, you could have the world being pulled apart by another very close gravity well (like another planet), and the gravitational pull of the two worlds could create a situation with floating landmasses. But this idea unearths a whole load of other problems and caveats, and it's worth its own question on here.
I hope this helps.