The temperature data above is for Belize City, which is on the coast and about 40 miles away, so San Pedro is similar, though maybe a bit cooler by a degree or two. Still, as you can see, the temperature range doesn’t vary much from one month to the next, so really the main thing to know about here is the dry season vs. the rainy season.
This whole area is fairly dry from January through late May, and the rest of the year is considered the wet season. The island tends to get heavy rainfall in short bursts rather than steady drizzles all day, so it’s usually simple enough to take cover for an hour or so. Much of the rain falls overnight as well so it’s not really as bad as it might look, though it does get quite humid during summer so make sure you book a hotel with A/C if you want to sleep.