You may simply be buying more food, and more protein foods.
When figuring out how much you spend, be sure to consider how much you spent each week on fast foods at McDs, BK, Taco B, Pizza Whatever...
Also, a box of Mac & Cheese is always going to be cheaper than chicken breasts. They are just different foods.
Canned tuna (water packed) is a fairly inexpensive protein source if you shop for buys. Eggs are good also--you can usually get a dozen eggs for under $4, even if you shop free-range.
As the other posters have said, buy in bulk and with foods like meats, freeze what you won't use immediately.
It will take some time and planning on your part, but you can do it. And you will be eating better. It's not uncommon for obese people to be undernourished at the same time.
"My religion is kindness." --His Holiness the Dalai Lama