I totally agree with the above recommendations, but, a couple of things....
1) You're going on vacation - to Belize! Does it really matter it you pay twice as much for some grocery items during that week in paradise? Think of it as helping the local economy. US items are more expensive than local, Mexican or even Danish or New Zealand imports; try something new.
Sure, you think you're going to save some money by eating at your villa, but frankly, you're talking about what - a couple of meals? You'll be missing out on some great experiences if you don't go out for dinner. And those meals out will likely cost less than if you were buying them in the US.
2) There is thankfully no Krogers or Winn-Dixie on Ambergris Caye. If the reduced selection found in San Pedro grocery stores is going to ruin your vacation, Belize may not be your ideal get-away destination. Puerto Vallarta already has a Super Walmart and Sam's Club....
Forget the agenda of preparing that perfect stateside type meal and go with the flow. Make grocery shopping part of the cultural immersion of being in Belize - if the store doesn't have what you want, improvise! You'll love it. Sure the stores are funky, but that's part of the charm of San Pedro. Where else are you going to find all the major grocery stores owned and operated by Lebanese merchants?
3) Belize is a wonderful place, just don't let unrealistic expectations or constantly comparing it to other locations ruin the experience. On our first trip to Belize, we met a travel agent from Southern California that didn't enjoy the trip because all she could do was compare it negatively to other places. She complained about mosquitoes, the beach wasn't as nice as those in Hawaii, the restaurants weren't as good as those on St. Maarten - blah, blah, blah. She totally missed the beauties - the people, the marine life, the water, the birds, the casual lifestyle.
Enjoy your vacation - you're headed to a unique and wonderful island.