I went on the South Beach diet and lost two clothing sizes...unfortunately though, not cheaply. But it was worth every penny. Everything healthy seems to cost more than it's less nutritious counterpart - white bread vs. whole grain, fresh fruit vs. canned in syrup, sugary cereals vs. whole grain, and on and on. The exceptions: rice and beans. Both very healthy (if you get brown, non instant rice), but very filling, and both very cheap. So use a lot of those in your recipes if you can.
I also had a hard time trying to find deals. You can't combine coupons and sales for fresh fruits and veggies...only on snack cakes and chips. I would buy whatever produce happened to be on sale that week, since I eat pretty much everything. For example, my favorite veggie is asparagus, but I will only buy it when it is less than $2/lb (still expensive, but I really like it!). Green beans can be found very cheaply - as can potatoes and carrots, but those two are not good for a South Beach-type diet.
Can you garden? We grow tomatoes, cukes, peppers, green and yellow beans, lettuce, spinach, swiss chard, beets, zucchini, squash, herbs...probably a few more I forgot to mention. I am even looking into a pear tree - but we have the luxury of a lot of land. Saves us a ton in the summer (and winter since we freeze a lot) and these foods are all great for you. If you can't garden, look for a local farmer's market to get these things.
Of course, the best way to lose weight is to eat less, which saves money too
All that being said, for me, the extra money was well spent. I can't tell you how much I enjoy the compliments I get now - not to mention my improved cholesterol. Good luck!