You can ship thru the cargo division of American Airlines. As long as each box is not over 70 lbs....it isn't real expensive.
Contact the cargo division at American and see what they say.
Whatever you do, don't go through XPresslane in San Pedro to ship your stuff; she's way too expensive and has a bad reputation for not doing her job well. She also has all these "hidden" charges and will hold your household goods hostage until you pay up. Not a nice or reputable way to do business.
I've heard good things about Mike Singh/Jose Gomez at Belize Transportation Agencies can get whatever you want to Belize the cheapest and most reliable way there is. Contact them at 011-501-2-73507. Or check out the website at www.belizetransportation.com
Another shipping company that trucks to Belize is Wingbridge is (561) 745-3134
Fax (561) 745-3134
Amerijet flys out of Miami and has the most reasonable air freight prices to Belize. You can check them out at their wesite at http://www.amerijet.com
You will probably have to hire a Belizean customs broker also.