http://cayecaulkerweather.com/weatherdata/caye-caulker-belize-live-weather-data.htm

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Here is another good weather site :

Caye Caulker Village, Caye Caulker, BELIZE DISTRICT -

Current conditions

Weather History for Caye Caulker


It has even has a camera working all the time.
The camera URL : http://www.wunderground.com/webcams/CCWeatherGuy/1/show.html