Cheap weight loss diet:
Eggs
Whole Grain breads
don't skimp on the protein
Chicken
90% lean ground beef (on occasion)
Water
Fish/flax oil
Don't use butter
don't eat a ton of starchy foods (potatoes..things with a lot of flour in them etc)
Salad... eat a lot of it... basic idea - darker green, more lean
Don't eat excessive amounts of fruits. Glycogen (the sugar) from fruits builds up in muscle tissue, and when it is not utilized, it nearly immediately converts to fat. Just like candy.
Keep potassium intake up - banana 2x a day could be a reasonable cheap way to get it, just don't over do it (glycogen).
Drink coconut water - It's a natural laxative, so don't completely over do it, but it can promote weight loss. A 24oz can is 99 cents. If you have a Spanish market or international food store around, shop there. You will probably find the most fresh and less pricey foods.
Caffeine - coffee once in the morning with no sugar or cream can assist in weight loss
go with what the others are offering for information as, I am by no means an expert at this as I imagine some of them are. I just happen to know a few cheap work-arounds.