We did the 2nd week in May back in 2003...it was hot! I had done my research and didn't expect it to be too hot but that week it was and it only rained once on a Thursday afternoon for about an hour. Crowd levels were moderate, but on EMH days it was high.
Crowd levels should okay, moderate I would say but very bearable.
Weather , probably just starting to hot up for the summer I would say, early months of the year are a little bit unpredicatable but would say usually May would be mid 80's.
It was warm & humid when we were there in May a few years ago. It rained almost every day, but it was just a 30 minute or less downpour and then it would clear up. Disney sure sold a lot of ponchos. My advice--take waterproof sandals (that way you don't have to walk around all of the puddles and you don't have to be in soggy shoes & socks).