We live about 40 minutes from WDW, Normally from June on we are in the "rainy" season, and the weather channel always shows thunderstorms in the afternoon, every afternoon.
Dont let that scare you though, because even if it rains, its usually a brief shower and then the sun comes out and dries everything up. Only two times has the rain affected us at WDW. Once on Test Track, they held us up because of rain, but as soon as it stopped we were off again, and once at Fantasmic, they almost cancelled the show, but the rain stopped and the show went on.
It has been pretty hot here already, so the showers are a welcome change, and it really cools everything off.
So that being said, stop looking at the weather, and enjoy your trip.