The paleo/primal restrictions on different foods really come down to one thing: inflammation.
Refined carbs -- sugar, high fructose corn syrup, white flour, white rice, etc cause inflammation. So do proteins humans aren't all that well adapted to, such as gluten (grains) and lectin (raw beans & legumes).
In addition, many types of fats cause inflammation: the unsaturated fats (polyunsaturated, monounsaturated, hydrogenated, trans-fats) are unstable and don't have a long shelf life before they become rancid. In addition, their ratio of omega 6 to omega 3 fatty acids are too high. To avoid inflammation you want fresher fats and to have a daily 6:3 ratio as close to 1:1 as possible. Most Americans eat closer to 6:1 omega 6 to omega 3 fatty acids. This is why fish oil tablets, high in omega 3s, are a recommended supplement. But you can go a long way to improving the ratio yourself by avoiding the bad fats. In general, don't use any vegetable oils at all unless it's either olive oil, coconut oil or avocado oil, and then opt for "extra virgin". This simply means the oil is less-processed. In addition, consume saturated fats from animals, such as butter, ghee, lard, and meat fat & skin. The grass-fed debate is actually about the same issue. Pasture raise cows and chickens eat the food that's natural for them. Cows are supposed to eat grass, chickens are supposed to eat primarily bugs & larvae. We feed them grain because it fattens the cows up and is cheaper & easier to feed mass-produced chickens a grain mix. But these diets do alter the meat & eggs, tipping the omega 6 to 3 balance in the wrong direction. So the fat in a grass-fed beef steak has a better (lower) 6 to 3 ratio than a steak from a cow that ate primarily grain.
Why is inflammation so bad? It is believed that inflammation is the root cause of many illnesses, and a driving force of the aging process. It can also compromise your immune system.
From my standpoint, I try to keep my omega 6 to 3 ratio low primarily by avoiding vegetable oils and supplementing with high omega 3 tablets. I also only eat free range eggs. I sometimes eat grass fed beef, but it doesn't taste as good so I'm not terribly picky about that.
Now as far as weight loss goes, primal/paleo works mostly because of the reduction in carbs. This is also why Atkins worked, although there was no focus on healthy vs unhealthy fats in Atkins, and Atkins is a truly ketogenic diet (less than 50g carbs on average per day) whereas paleo/primal is not (average between 50-100g carbs per day for weight loss, 100-150g per day for maintenance). Paleo/primal is also much easier to maintain than Atkins.
It certainly worked for me. I do let a few grains sneak in now and then, as well as cheat occasionally with a dessert. I am not lactose intolerant so I eat dairy. Cheese, whole milk (skim is basically sugar water), and Greek yogurt, which is a staple for me.
I like paleo/primal. There's a lot that makes sense about it -- you really can't go wrong focusing on whole, healthy foods. I'm not a 100% adherent to it as I said. But it does work.