Both of our trips have been in early June and we have found the weather and the crowds very manageable. It generally rains for about 20-30 minutes once every day. We usually only wait about 20 minutes for most rides and pick up FastPasses if the wait is over 30 minutes. We have always been able to see and do everything we want. Just be aware that Gay Day is the first Saturday in June at MK and I have heard that it can get very crowded.