My husband and I are on a relatively slim budget (we're both on disability). We can and like to cook, but because of our health issues also have to take advantage of a lot of easy-to-prepare, not-really-cooking-at-all meals.
We've learned thousands of ways to cut corners when it comes to food costs and food preparation.
There are times when we do absolutely no real "cooking" for days (if not weeks).
Counting plans whether they be calories, weight-watcher's points, fat grams, carbohydrate grams, or exchanges (my preference) are all low-cost options. All the information is available for free online (Weight Watcher's isn't free, but their current and past program information is. All you need is online access or a library card).
It may not seem like, because it seems like (and is) a drop in the bucket compared to all of the information on eating unhealthy, or dieting expensively, but there really is tons and tons of resources for budget-dieting.
It's only a matter of seeking them out (and learning where to look). They're not hard to find (especially if you have online access), but does take a little effort and practice.
You have to look at grocery shopping, food preparation and eating for health and wieght loss a little differently. Making it an enjoyable challenge as much a possible, works better than viewing it as a miserable, impossible chore.
To get you started, you might be interested in the shoestring-meals forum, where we share money-saving tips and recipes.
http://www.3fatchicks.com/forum/shoestring-meals-235/
Lots of great tips for dieting on a small budget.