I have been going in September every year since 2009. We always go the week of Labor Day. We are a party of two.
Weather - It is Hot. It is fairly dry, for Central FL anyway.
Crowds- Relatively speaking, very low. Unofficial Guide says the lowest of the year. We have walked up before to, say Rose and Crown, Brown Derby, and been seated immediately. If you look online right now, there are openings at Le Cellier for Dinner for two, in spite of Free Dining being offered on those days (that may say more about recent changes there, risotto, credit/pricing, etc.) If you haven't booked ADR's, I would right away if you plan to. I have seen a 20 minute wait posted at Everest in late morning/lunch that was overstated. I have seen Soarin' at 20 in the middle of the day as well, although not typical. Toy Story still gets long waits. Resorts are not crowded, nor is transportation. Many special events speckle the month, so look for shorter hours some days.