Our WDW vacations are always during the last week of May through the first full week of June. Gay Days is the first weekend in June. I believe that the crowds are affected by the extra visitors. We just avoid the Magic Kingdom that weekend.
The heat and humidity doesn't bother us too bad but we are from Louisiana where our June temperatures reach almost 100 and the humidity is super high! I think the Florida temps were in the high 80s and low 90s.
Over the years, we've seen the crowds grow. By mid-afternoon, the most popular rides have long waits but are manageable if you use Fastpass.
We take two days for the Magic Kingdom, a day for Hollywood Studios, a day for Animal Kingdom and two days for Epcot. We also take several days to just chill out, take in a water park, shop at Downtown Disney, etc.