I have flown US Air to Belize now at least 16 times in the last 2 years, and NEVER had a problem (until my last trip which was Saturday). My luggage didn't arrive with me in JAX, but it was delivered the next day.
I travel with my in-cabin pet, and always have over the weight limit. Never had a problem, at all.
I think you might find that while several have those rose-colored glasses on concerning Belize, it's not all wine and roses, the political turmoil does exist, the GOB is having problems, and it does remain a third world country.
Does that make it less desirable for tourists? I don't think it should. It's still a beautiful place with SOME wonderful people. Just don't forget that "sh** happens".