Who is the god of weather in Greek mythology?

I don't think there's a god or goddess for weather in general. There are gods for various aspects of weather, but the whole of weather is a result of them all working together.

In fact, there were even different gods for different winds. For example, Zephyrus was the god of the west wind, and Boreas was the god of the north wind. (Notus and Eurus were the south and east winds respectively.) Zeus was a god of rains and storms... particularly thunderstorms... and Apollo was the god of the sun.