It sounds fine to me.

I would agree that "the weather is a bit windy" is a little odd. Usually people ask the question "What's the weather like?", and the response is something along the lines of "It's windy/cold/chilly/humid". However, it's worth noting that some people might not find your original sentence odd. I just believe that "the weather is a bit windy" is what would be heard more often.

Isn't it more correct to say, "It is a bit windy"? The weather is good or bad. The weather is not windy. It is windy. The "it" is a formal subject and is not a pronoun for "the weather".