We were there last Sept and liked it so much we are going again this Sept ....
The weather is humid and hot, but not like july or august. September is a very unstable month, so you don't know exactly what to expect. It is also rainy / hurricane season. Last year we were there when a hurricane hit and it was one of our best trips to WDW....on the plus side of going end of Sept: The parks are not crowded, it's not as steamy and it's "value" season. Also I don't know if it was the incoming hurricane, but the pictures we took were spectacular because of the sky and natural lighting...they look like postcards.
So not to worry, if it rains in the afternoon, it just cools everything down. Last year during the hurricane, people were checking out in droves...we added 2 days! We changed our flights, no charge due to the weather and got a free day added to our parks tix. The weather was beautiful and the parks back to normal the next day. Just some FYI in case it happens to anyone while down there. Don't check out and go home, stay and have fun, Disney throws a great "hurricane party"!