I don't know how I should interpret this :
For simplicity assume hypothetically we make multiple copies of earth:
XS, S, M, L, XL. The only difference between them is their size
(radius), everything else is the same.
So basically, the only differences with these new Earthes and M Earth is that their volume and mass are divided or multiplied by 8 or 64.
In that case, be aware that you should prepare for a variety of noticeable differences... Damn, multiply Earth's radius by 4 and the only thing that would remain might be the spherical shape. Might.
In the end, it's mostly a matter of numbers :
- Weather depends on climate.
- Climate depends on temperature and atmosphere's composition and pressure.
- How big the atmosphere is depends on gravity. That's why some planets are called Gas giants. They are so big that they attract a lot of gas, and at some point that gas is most of the planet.
So it all comes down to haw gravoty applies :
Gravity increases with the mass of the involved objects and decrease with the squared distance between them.
Since volumes is in cubic meters, a growth in radius means that the volume grows by the same amount but cubed. Mass follows directly (hum... until some point, but we'll come to it later...) volume, so same thing for mass.
From this, we deduce that doubling the radius of a planet multiplies its mass by 8, meaning that from the same distance, the second planet has a 8 times stronger gravity. The planet's surface being 2 times further, it divides the gravity on the surface by 4 times more. The reuslt is 2 times stronger gravitionnal pull at the surface.
With a planet 4 times bigger, that makes 64 times the mass and a squared radius 16 times longer, thus a surface's gravity 4 times stronger.
So gravity on the surface grows directly following the radius, but at identical distances, it follows radius' increase to the cube.
That means that your L and XL planets will capture a lot more gas, while S and XS not that much, and they might even lose whatever atmosphere they had at the begining of your thought experiment.
More gravity and more atmosphere mean more pressure. If some gases have greenhouse effects, more of them also means more greenhouse effects thus higher temperatures overall - and less day/night differences.
You can actually have a planet so big that it attracts so much gas that **gas pressure is high enough to crush you. Or your car. Jupiter is like that. Any probe we could send to it would be crushed and even melted way before reaching its surface. That's how dense gases can get when as gravity rises - and we aren't at star-like gravity, only planet-like. Since pressure means more things in a reduced volume, that's in fact increasing the effects of gravity : by falling to the planet, crushing the gas below, and getting closer to the surface, being crushed by the other layers of gas above, the overall gases are more and more affected by gravity as the distance is reduced. Combined with the cube/square law, that makes size an escalating issue in solar systems.
To conclude : dividing or multiplying the radius of your planet by little numbers have mind blowing implication, turning them to either sterile moons or crushing gas giants. Our own planet would quickly become sensibly less hospitable to us if it radius was slight different in either direction, since we evolve to fit that range of pressure.
Pressure and temperature also have to do with state change : as pressure decreases and/or temperature increases, matter will reach/approach its liquid or even gas state, and the other way around. But if pressure is quite low, there is no liquid state at all. So if your planet is too little and
doesn't have a significant atmosphere (like the Moon), there will be no liquid water on it. With too much pressure, you will be stuck with ice except if the water is heated a lot. And melting is what consumes most of the energy, not rising the water's energy, just changing its state.
To sum it up, if you intend to build a planet with climate, life and whatever based on water and would prefer it to be realistic, stick with an Earth-like radius : 2 times Earth radius is HUGE ! 4 times is COLOSSAL !
If you want a planet two times bigger, double the volume (and mass) instead, I believe that's what you actually had in mind.