Early May is a great time to visit Florida. The snowbirds have returned back up north, kids are still in school and most college kids are still taking exams. All of this means less people in the parks and typically less cost on airfare, hotel rooms and car rentals. The added bonus is it usually not super humid yet.
On the contrary, September is hot, humid, and it pretty much rains every afternoon or early evening. Add in it's also peak hurricane season. It's less expensive to travel and stay in Florida then but the weather stinks. As a Florida resident I'll admit if I didn't have a kid in High School I would bail and get out of Florida in August and September if I could.