You can lose weight on the paleo diet. Expect a steady pace, faster initially and then slowing a little as you get nearer to your optimal weight. Here's something about why. Calories do matter, it's just not something you have to count. The trick is that when you've eaten a paleo meal you'll feel as satisfied as before, but on less calories. Also, on the paleo diet you'll be cutting down on the recreational eating - you primarily eat to stave off hunger, not for fun. Snacks aren't for fun, but to kill hunger.
When you're trying to lose weight eat only when you're hungry - don't eat for fun (except occasionally). Don't stuff yourself like there was no tomorrow:. Remember that your next meal is never further away than the snacks (real foods) you always keep with you. Try to eat just the right amount to make the hunger go away - with the knowledge that you can always snack between meals. This should help making your stomach shrink. Feeling full and satisfied is the key to success on this diet, and you have to teach your body that paleo foods are what makes it feel good (because that's what they do!)
Always eat mixed meals with lots of vegetables. Eating "only" meat is likely to get you killed in the long run unless you possess the specific knowledge of what to eat on such a diet. The traditional winter diet of the Inuit isn't made up of skinless chicked breast morning, lunch and dinner - it's far more sophisticated than that. Eat mixed and you don't have to worry about getting sufficient nutrients. Personally? Well, I am not a big fan of vegetables, but the meat and fat sorta makes up for it, complements it.
Remember that after a week on strict paleo foods everything will change. You will feel very different and the way you experience hunger and eating will be different - it will be better and more manageable.
You'll be eating very different foods than you're used to. Start out conservatively and see how much you need to feel full. E.g. don't panic and make 6 eggs and 12 slices of bacon, even if you can stuff it all down. Make 3 eggs and 3 slices of bacon for breakfast and see how far it'll carry you. You can always supplement with snacks (fruit, meat, nuts, carrots) if you happen to get hungry soon after breakfast.
You get a metabolic advantage by eating more protein, but there does not exist any other magic metabolic advantage. What you gain on protein here may even out with your slightly increased fat consumption which has a lower thermic effect than carbohydrate. Protein has a thermic effect of 25%, meaning you only get 75 g. of effective energy from 100 g. protein eaten. Carbohydrate has a thermic effect of 15% and fat 0%.
Your body will be more conditioned to burning fat for energy when you stop relying on sugar/starch/complex carbohydrates for energy. This may aid your weight loss as the body will have no resistance to losing your fat stores, but it is not scientifically know. Most likely, when your body adapts to the new diet you'll just feel better.
The low levels of insulin in your blood opens up for the fat burning process. Again: most likely to make you feel better, but it doesn't change the energy needed and expended Fat and adequate protein will prevent loss of lean body mass. The diet does not lower your metabolism because you eat plenty of nutritious food.
(Complex) carbohydrates are just complicated molecular arrays of sugars. When absorbed by the body they are converted to simple sugars. Humans can taste simple sugars as "sweet" on their tongue, whereas a potato doesn't taste sweet despite producing a big sugar load on the body.
You eliminate high-carbohydrate foods that used to provide you with vast amounts of calories. Protein and carbohydrate are 4 calories per g., fat 9 calories per g. Try to do the math yourself, e.g. by entering two sample days on Fitday. One such comparison I did showed I now eat 1000 kcal less per day.
With the paleo diet you will be free of addiction and your appetite will be stabilized. And you will not feel hungry, despite eating less calories.
Insulin is a special player. It's a hormone primarily responsible for eliminating blood sugar from your blood. Its secondary function is to transport amino acids to your muscles, and also to store fat. When you eat bread or a baked potato you cause a sudden, dramatic rise in blood sugar, and your body responds by frantically producing insulin to remove this dangerous substance from your veins.
For some people -- especially those of us who tend to get overweight by overeating -- this insulin surge causes an unnatural lowering of our blood sugar, making us even hungrier than we were before. Which means you eat much more than you actually need, and that you get hungry again too fast (which is why people often drink cola or eat candy to fend off the "sugar cold", yet they only feel good when they're eating/drinking constantly).
These rapid rises and falls in blood sugar cause something akin to an addiction to sugar. You end up chasing that sweet sugar high.
Your body does try to protect itself from obesity by becoming insulin resistant on the sugar pumps. However, this tends to start a dangerous arms race between your insulin producing pancreas and the sugar pumps in your blood veins. In time this often causes diabetes 2 in people, a.k.a. "old man's diabetes". Even young people are today struck by diabetes due to all the cola and complex carbohydrate junk they eat.
Willpower is not needed in the same amuont as with other diets, as your addictions will fade in a few weeks, and you simply do not starve on this diet. (This is NOT the inhuman and degrading Fat Club).
Coffee can disturb your appetite by provoking a noticeable insulin response that eventually lowers blood sugar levels (makes you hungry and moody), although some research shows coffee actually increases insulin sensitivity - but the result may be the same lowering of blood sugar. You should remind yourself that if you get hungry shortly after drinking your morning coffee, it is not because you need food. Coffee is not allowed on the paleo diet, but most people drink it anyway.
Alchohol can have much the same effect as coffee. It gives you the munchies, and often you start craving some of that sweet carbohydrate (pizza anyone?)
Protein and fat make you feel sated quickly and for a long time, but it is important to have both fat and protein in the diet. Lean protein may actually make you feel sated quickly, but without the fat (and the added calories) you won't feel full until your next meal, so take care not to lower calories too much. Neanderthin dieting should not be low fat but medium to high.
Some theorize that your body can sense the extra nutritional value from paleo food, and that this make you feel sated more quickly. I'm not sure that's a true theory.
You generally do not need to put an effort into getting enough fat. With the fat on animal flesh, nuts and the oil on your salads you should be covered adequately, provided you don't restrain yourself excessively due to the old "fear of the fat" attitude.
Calories matter to some degree, just not as much as on a "normal" diet. You'll find that you lose weight on a higher calorie count, and you'll find that you normally won't noticably gain weight if you eat too much, just stall your weight loss. It is possible to eat so little that you lower your basic metabolism, but this should and must not happen. Most of the time people stall in their weight loss it's because they eat sufficient energy from dietary sources.
Nuts are allowed, and they're vital as snacks for the modern caveman. However, they contain a lot of oil. Eat too many nuts and you'll meet your body's energy needs exclusively through your diet. That way you do not metabolize your own fat for energy. Eat half a handfuld at a time and let 5-10 minutes pass and see if the hunger goes away. One handful of nuts will weigh approx. 30 grams (about and ounce). Calorie-wise a 30 g. handfuld of hazelnut/filberts is the same as 320 g. of apples or 435 g. of carrots.
Bacon can do a bit of the same as nuts. It's very high fat, salty, and you may end up eating many more calories than you expected. Sausages, spare ribs and pork rib roast fall in this category as well.
Fruits are allowed on the paleo diet. Eating too many may slow down your weight loss, and you might wish to opt for a more "winter diet" scheme, ie. eat only meat and vegetables. Fruits may be a big problem if you're very insulin resistant or if you suffer from diabetes. Dried fruit and honey are not recommended, except occasionally, due to their candy-level sugar. Go easy on the bananas and other starchy fruit. Notice how this advice also effectively restricts calories.
The simpler you prepare your food, the better from an overeating point of view. Remember that in nature a starchy food is also never fatty, a sweet (fruit) never also fatty. Processed foods easily violate this principle and disturbs your natural appetite. Danish pastry e.g. is loaded with simple sugar, starch, salt and fat. Potato chips are loaded with both fat, complex carbohydrates and salt.
Excessive use of salt is not only unhealthy, but it screws up your appetite as well. Everyone knows the addictive properties of pistachios. If at all possible, only eat unsalted, natural nuts (or be prepared to muster some of that old will power). Pork rinds are OK too, but go for the least salty and least fatty ones: most do not need pork rinds with 50% fat by volume. (I've noticed that the "fluffy" ones are the least fatty.)
Consider getting a food dehydrator for making your own jerky (dried meat). It's a great hi-protein, low fat, snack that stores conveniently. Jerky can also be used to make pemmican.
Body composition may change during the diet. If you want complete knowledge about these changes, get tested at your local gym or buy one of the cheaper (and more inaccurate) weights that also measure your body fat percentages (they do this by sending an electrical current through your body).
Generally don't use all sorts of Power Bars and other refined low-carb products. The culprit is often the sugar alchohols, aka sorbitol and maltitol. Some people do not digest them, others actually do. For some they cause a blood sugar rise.
Exercise is not necessary to lose weight on this diet. Generally speaking fat people tend to be in such a bad shape that any exercise doesn't really contribute much to weight loss. Actually, if you're very overweight and exercise very hard you may easily end up hurting yourself. Exercise in moderate amounts is of course healthy for a lot of things, and you do not need to work out extremely hard to get good health benefits. Our ancestors tried to relax most of the time, and the exercise they got was mostly walking and the short bursts of explosive energy when trying to kill their prey (or trying to escape from being prey themselves). Weight or resistance training is generally encouraged as an efficient way to get in shape and build muscle.