This is interesting - are we sticking to $3 per meal, or $65 per week? Because bulk buying rice and grains and pulses, tins, stocks, spices, etc helps a lot. You then buy fruit and veg daily / weekly. You use meat that can be turned into several meals - buy a chicken and roast it. Use the left overs for sandwiches. Boil the carcass for soup.

($65 per week is £40 per week. That's doable.)