Sometimes eating "cheap" is foolish when it comes to being healthy. Cheap meats like ground beef and hot dogs are horribly bad for you but they seem to be the go-to proteins for people trying to cut back on their grocery bill.
Beans and rice, quinoa, eggs (separate and use only half of the yolks), smaller portions of beef/pork/chicken and adding more vegetables to round out your plate can extend a budget but remain healthy.
The other quick fixes include eliminating bottled beverages, chips and cookies, luncheon meats and deli cheeses, bakery goods and convenience foods from your shopping trips. The more that you do "from scratch", the more control you will have over what you're putting in your mouth and the less you will spend at the check-out.
Learning how to slow cook the tougher cuts of meat will make them more palatable. Growing fresh herbs and using them to add punch to your recipes also helps. Soups and homemade breads make for great dinners on cold winter nights. They use less meat than you would include in a meat & potatoes dinner but they are very filling. They also use the pieces of meat that are too small or left over from other meals.
Lastly, assess how much food you're throwing out due to spoilage or because you made too much. Either adjust your recipes down so that you prepare less or else begin to freeze leftovers in easy to reheat portions.