Have you thought about shopping at one of those places like Costco, Sam's Club and BJ's? Their meats are a lot cheaper than at the grocery store! So are their vegetables. You could buy those in bulk, then blanch and freeze whatever your family can't eat right away (as opposed to letting it spoil since there is so much).
I spend about $150. to $175, a week feeding 3 adults and 2 teenage boys. Nonfoods household supplies also are in that bill. Of course, I use coupons and get a 10% discount because I work there full time and that helps!