The first Saturday in June is considered Gay Day at MK. We were not aware of this our first trip in 99 and found out after we arrived. I'ts really no big deal, most of the couples generally keep to themselves. MK will be extremly crowded that day, upwards of 100,000 people, but the other parks won't be to bad.
As far as the weather goes, we had great weather in 99,00,01. I'ts usally Florida's dry time up to the end of June. We never had any significant rain during our stays. The temp usally was in the mid to upper 80's.
The parks were never overly crowded, average wait time for the rides was about 20-30 min.