DD44,
June to November is the hurricane/wet season. Weather is HOT. We don't get all-day downpours, nor do we get rain for days on end. When it does rain, it's usually overnight. The wet season is not all that bad here. As for hurricane, September & October are the months of greatest probability. In the 100 or so years of records, there have been only about 4 hurricanes before September.
I like the period from November to April because the days aren't sweltering hot, and the nights are cool enough to sleep without an a/c. At least that used to be the case. In the last couple of years, I've had to use a fan at night in January. But Dec to April is also peak tourist time, so accommodation rates might be higher.
I've always found May to be the hottest month of the year.