You people crack me up. And, I am not just refering to you Polento as others have ask this also. There are trained meteorologists that can't predict the weather accuratly for the next day and you are asking people on this board to tell you what it is going to be like months from now. Some even try and tell you.
Yes, it is the hurricane season from June to November but you can have some of the best weather those months and you can have some worst, except for a hurricane, almost any other month. The only thing I would offer as far as any prediction is that the odds of having good weather are in your favor any time in Belize. I would not let trying to predict the weather determine when I would go to Belize. Go when it is the best time for you.