TacoGirl has done a recent write up of cost comparison of the Belize cost of living. It gives you an excellent and detailed look at the premium you pay on certain items.
I think however it misses the point that if you chose to live in Belize, you are making a distinct choice to not live on the same brands that you would normally live on in the United States. While brand for brand prices in the US are cheaper than in Belize, you often will elect to buy a local brand alternative instead of the US brand, which is often comparable or cheaper... and certainly cheaper than the name brand as found in Belize.
I haven't done an exhaustive side by side of US brands to Belize brands, but did happen to locate a receipt from Super Buy South that I received on my last trip there in September. I figured I'd share some of the prices I paid. All prices are in USD.
$0.55 Mac & Cheese - 1 box
$1.34 Light Beer - 1 bottle
$1.35 Milk - 1 pt Vitamin D
$1.07 Black Beens - 1 can 400g
$4.02 Boneless Ham Sliced - 1 lb
$3.45 Polish Sausage - 1 long ring
$0.75 Rice - 1 lb
$1.35 Refried Beans - 1 can 440g
$1.15 Paper Towel - 1 roll
$0.45 Margarine - 1 stick
$1.25 Hot Dogs - 1 package
$1.07 Cookies - 1 package of strawberry creme cookies
$1.25 Hot Dog Bread - Don't remember quantity, but a package of maybe 6-8 large rolls
$1.37 Tomatoes - per lb
$1.25 Carrots - per lb
Now Super Buy South is not the best place to pick up certain things at the lowest prices, but this hopefully gives you an idea of what to expect.