Island weather is pretty much near perfect all the time! Although global warming can at times make things unpredictable, the driest months on the island are normally from Christmas through May; if it does rain, it’s usually very short & sweet. June through mid-December is “rainy season“, but even then when it rains they are usually brief, although heavy, storms.
There is a hurricane/tropical storm season, which officially is from June through November. (Traveling during this time? Definitely consider trip insurance.) There’s some interesting history on hurricanes and tropical storms that have affected Belize here; the latest was Hurricane Lisa hitting November 2, 2022. Belize’s National Emergency Management Organization keeps everyone well informed should there be any ‘situations’. There is also an informal Belize Hurricane Watch Facebook page here you can follow.
The more popular online weather sites often show the weather information for Belize City, even if you have asked about San Pedro, Ambergris Caye. Want to know what the weather’s really like on the island? Try WindFinder and/or Windy.