I've been to BElize three times in September. Rain was never a problem. The sea breezes die down though, it's one of the few months I've used air conditioning when I've been there. And, do watch the forecast for the occasional tropical storm/hurricanes that can show up.

Yes, the water stays warm year round. January air temps can be cooler, although this past January was very nice. I think I read water temp then was around 78F. In September water temp is well over 80F.

We've visited twice in July/August - hot and humid with rain almost exclusively at night. Technically June through November is hurricane season and later in the season you're more likely to see storms.

My photos, blogs, and travelogues are below if you're interested. Happy trails!
http://www.flickr.com/photos/staceyholeman/collections

Thanks, guys; I appreciate all the good info.

Do things shut down at all during certain months? We went to the Caribbean in September and several restaurants, hotels, snorkeling companies etc. were closed for the season. Does that happen at all on Ambergris or other cayes?

Yes, some companies close for repairs or their own vacations, but there are plenty of other businesses who stay open year round.