The wettest months are from June thru October, although you'll usually also have a fair bit of sun during this time. One benefit of traveling to Belize during the low season is that it is less crowded. Historically, Belize's hurricanes have arrived in September and October.
Belize is considered sub-tropical -- temperatures range from 50-95F degrees. November thru January are the coolest months, averaging about 75 degrees. There was a cold snap in January with uncharacteristic lows in the mountains of the Cayo district. If you plan to travel around Belize, be prepared to dress for cool and warm weather as temperature can vary greatly, depending on location.
Belize's water temperature averages between 79 and 83 degrees.