There are several novels about ocean planets or planets with only small islands. I never felt it needed any kind of special explanation. If the Earth had only a bit more water, we'd have something like an island planet, because only the mountain ranges would look out.
As for the weather, there are two things that I can think of. There is a lot of rain on islands because of the surrounding mass of water. Look at pacific islands.
And there will probably be a lot of wind, always from the same direction (East). The Earth's rotation is causing the atmosphere to "slip", and on the surface that "lag" of the atmosphere is perceptible as wind. On the Earth that planet-rotation-wind mostly happens in high altitudes, because mountains and the high and low air pressure areas that are caused by the land masses break that wind closer to the surface. On a planet with a plain and uniform surface there won't be anything breaking the wind and it will be strong and continuous. On Earth, that wind is called "trade wind".
Vegetation will adapt to that wind. On Earth you can see this in windswept trees, or, if the wind is stronger, in trees only growing in the cover of ridges.
There will also be a lot of rain on the windward side, but only to a cetain altitude. Above that will be very dry.
The source page for that image explains the phenomenon in detail.
In genereal I would think that researching the climate of pacific islands will give you a good idea of what to expect on an ocean planet.