Most hotels, even tiny places, in Belize will do your laundry for you (wash and fold kind of thing). Some do it on-site, others get local people to "contract" it.
My opinion is that if a hotel in Belize, where a lot of people could use the money for doing laundry, can't have your laundry done at an affordable price, it is not offering the service it should be and is probably weak in other services areas. Even when I'm traveling on a budget, unless I'm staying in a rental house or camping out, I don't have the time or inclination to do my own laundry.
--Lan Sluder
Belize First Magazine
http://www.turq.com/belizefirst/