Ok, allready found an answer. There is sth wrong with the leaflet.css file. You have to just delete the leaflet.css library link in your code:
This can be caused by anything. But my first idea was that Windy API uses modified CSS. If you are doing everything right, try to check if it is not hidden by CSS. Otherwise, it would be great if you can provide us with some working example (only leaflet, without Windy) and even with non-working example (including Windy).