The Paleo Diet (or something similar) has also worked well for many people in losing weight and just feeling better overall. The culprit seems to be less about calories and exercise than about eliminating carbs, sugar and processed foods.
There is quite a lot of anecdotal evidence to support this, and I can just add that my wife and I started on it nine weeks ago and we have never felt better. I even dropped a few pounds although I didn't really need to. We also supplement with probiotics to ensure that we maintain good levels of healthy bacteria in the gut, which is where much of our immune system functions.
I'm currently doing a Keto diet (very similar to Paleo) and -at least for me- this is definitely the case. I'm addicted to carbs. I cut carbs and I immediately start losing weight and forget about constant hunger. Whenever I eat anything with carbs, my weight loss stalls and I start having cravings again, all the time.
Edit: Oh, and by the way, I've lost 40 lbs since I started :-)
I think one reason the paleo diet works for so many people is that most people are just bad at predicting the caloric content of food. So they think they are taking in about the same amount as before, but actually it has dropped significantly.
As an example: every single sandwich on the menu at Applebees, including the grilled cheese and the veggie burger, has more calories than the 12oz New York strip steak. The BLT has nearly 3x as many calories!
Another reason is that because it has such specific dietary guidelines, it tends to encourage people to prepare their own food rather than eat out. This alone drops more calories than people think, because of how most restaurants prepare food (with a ton of sugar, butter, fat, and oil).
I do agree that it delivers more nutrients than packaged food, which would improve health and make people feel better. It's easier to continue putting up with inconvenience if we feel better.
There is quite a lot of anecdotal evidence to support this, and I can just add that my wife and I started on it nine weeks ago and we have never felt better. I even dropped a few pounds although I didn't really need to. We also supplement with probiotics to ensure that we maintain good levels of healthy bacteria in the gut, which is where much of our immune system functions.