I have some weeks where I'm very under budget because I cooked enough for leftovers and other weeks where I go over because I need to stock up a little. We also still go out to eat most days and sometimes we adjust on the caliber of restaurant to save money for groceries. All in all it balances out to the same yearly budget we've always had.
The biggest change we've had is that I buy more vegetables than I used to. I can eat 3 snacks on one cucumber and it only costs me a dollar and change. In the fall I buy those little lunchtime apples (just small enough to be one carb serving) and get generic cheese cubes to munch on for snacks as well. All of this is very inexpensive, delicious and healthy.
I sometimes go back to canned and frozen foods. Broccoli, Brussels sprouts (no sauce), grilled chicken and turkey burgers are frozen staples in the house. When I have a lite extra cash, I'll buy a big bag of frozen, cooked, peeled & deveined shrimp. We always have canned green beans, tomato sauce, corn, black beans and soup in the pantry...all the low sodium versions ($0.25 more than the usual kind at most, but usually the same price). All of these things can be easily turned into lunch, dinner or snack at any time. I replace as I run out, so I don't have to spend a fortune in one trip restocking.
Healthy doesn't have to mean expensive. Notice I didn't say I buy low-carb this and low-carb that? First of all, low-carb products DO cost a lot more. They also usually taste like crap. I have yet to find a low-carb product I like. I buy whole grain foods which cost the same as the other stuff.