We too have sailed in June. The week we went it rained literally every day and enough to spoil some of our fun. However, Disney went out of their way to make it as enjoyable as possible. We almost missed Castaway Cay but ended up getting there later in the day. When the sun finally did come out (that one afternoon only) it was HOT. We have also been in December and are now going the first week of March. I know you have a chance of rain, hurricanes or heat any different times you go so I would just go when it was convenient and hope for the best. It is just SO MUCH FUN rain or shine, heat or cold!!!
This is a "make up" cruise from the one in June last year. Our daughter fell and had to get stitches in her chin while at XCaret and it kind of put a damper on all of our fun. I will say I sent a letter to Disney thanking them for the kindess of two of their employees and they sent a voucher for her to come back free. In return for their kindness, we are taken five couples with us that have never sailed the Magic before!!! The only drawback was we couldn't afford our cat 6 with verandah again because it had gone up so much but after reading these boards I am not worried about the cat. 9. Seems like everyone loves it too.
Go have fun.