Belize has a country a subtropical climate that is warm and humid and the trade winds bring cooling sea breezes. The dry season runs from February to May. The rainy season is from May to November, also containing the hurricane season (June-November), which brings coastal flooding, especially in south.
The best diving season is therefore from December to June. This is also the high season, so prices tend to be higher. The biggest influx of tourists is between mid-December and mid-January and around Easter. In May the warmth and humidity go up, but it is the month when winds are calmest and it is in the middle of the whale shark season, which runs from March through June (April-May most consistent). When taking all these facts into account, the best time to visit Belize is from March to the end of May.
If birds are your interest they are most abundant and varied during the autumn migration (late August to October) and around winter and early spring for migratory species.
Note that during the rainy season, rainfall is heavy, particularly in the south. The annual rainfall is around 1,27m (50 inches) in the north to over 4m (170 inches) in the South. The country has been known to be affected by hurricanes off the Caribbean Sea that tend to be very violent storms.