Hi! We were there this past September from the 9th-14th. We loved going during that time; we have already decided we'll be going back during that time frame next trip. The low crowds were great! We literally never had to wait in line for more than 5-10 minutes at the most--even on the most popular rides during the middle of the day. Since we're SO not crowd people, for us it was the optimal time to go.
As for weather--if I remember right, it rained only for about 1/2 hour one of the afternoons we were there. It also sprinkled for about 15 minutes one of the days. I was very suprised how little it rained (not sure if that's unusual or not??). We had brought with ponchos from home, but never once used them--never even opened them!
The downside is that it is hurricane season--something to always take into consideration. Also--it was quite HOT--however it wasn't unbearably so (in my opinion). We drank lots of water!!
Kelly