My fiancée and I spent 14 nights at the Beach Club from Sept. 1 through the 15 last September. I'm not disputing what anyone else remembers, but like dBugged, I don't really remember excessive amounts of rain or totally rained out days with ONE exception where it did rain lightly for most of the day one day (though I KNOW we were never stuck in our hotel room all day due to rain so if memory serves me, it couldn't have been that bad after all). In fact, I remember specifically thinking we once again had excellent (albeit very hot) weather for our annual Sept. trip (we go every year for the first two weeks of Sept. basically). I checked my trip report as well and don't have any mention of excessive rain, and in addition, we actually watched our home videos of the trip just last weekend as a warm up for our upcoming Sept. 2 through the 14 trip this year at AKL, and again didn't see any signs of disappointment due to rain. So can't explain what others who were there on the same dates remember as it's completely opposite what our experience/memory was/is. That's not to say it didn't rain, I just didn't think it rained excessively nor do I recall losing full days to constant rain through out the day.
In general though, early Sept is a great time to visit, weather can still be very hot, average in the mid to upper 80s with good chances for 90+ on any given day. As usual and as expected, brief showers occur almost every day, but are usually very short in duration, though it can REALLY rain hard during those showers sometimes.
Like others have pointed out, going in Sept. is a compromise, the parks close earlier, in some cases like the MK it can be MUCH earlier. MK closes so early in fact that most days in Sept. don't have fireworks or nighttime parade at MK, there are a few exceptions though. Epcot always still has Illuminations at 9PM though, as does Disney Studios with Fantasmic at least once a night. But the benefit to going at this time is the greatly reduced crowds compared to what you would have experienced only a few weeks prior. This means shorter lines usually and less waiting in general. The biggest most popular attractions can of course still generate long lines during peak hours of the day, but with less effort than is required during other busy times, you can really minimize the amount of time you spend standing in lines. And often, we find no waiting at all for even the most popular attractions during early mornings or early evenings.
So this is just our personal experience and we absolutely love going in early Sept. and have continued to do so for several years now due to the consistent good weather (again very hot though, but we like that), and low crowds. Good luck with your trip.
Mirth