Listen to your physician or tropical medicine specialist, or the CDC, but as a practical matter very few people visiting Ambergris Caye take anti-malarials. Malaria is present in Belize, and in fairly large number of cases considering Belize's small population, but one is at risk mainly in the far south and in other bush areas.
Even if you decide to take an antimalarial, there's no need to take Larium, as the strains in Belize are not chloroquine-resistant. Chloroquine (trade name Aralen) has been used for years, or decades, and most people have no reaction to it except possibly a slight upset stomach.
Belize First Magazine http://www.turq.com/belizefirst/