One of the major advantages of the low carb diet is that you can eat until you are no longer hungry. Compare this to a low-fat diet where you always crave for more food. You cannot, however, eat unlimited amounts. Let's just look at the pure "physics" of calories expenditure:

A healthy adult in their 30's will burn approximately 2000-3000 cals / day (the upper limit for males, the lower limit for females). If all of this comes from fat, we can theoretically burn 222 - 333 grams of fat / day (1 g fat 9 calories). In ketosis, fat is converted to ketones. As in all conversion processes, friction (or inefficiency) is introduced. 1 gram of ketones contain 7 calories. Subsequently, using the data above, in ketosis we can theoretically burn 285 - 429 grams of fat / day.

From this point on, the actual fat burnt is the difference between this theoretical value and actual grams of fat consumed. I know of people consuling 1 kg (2 lb) of cheese per day. This is approximately 300 - 400 g fat. These people will not loose anything.

Too little fat will also be a problem. If fat intake is sub-optimal, the body will break down three of the nine essential amino acids stored in the muscle into glucos. The result is that muscle is used instead of fat. In my experience, working with over 100 people from all walks of life, optimum fat intake is 70% of the theoretical maximum, 200 - 300 grams fat / day. This will allow for a fatloss of 85 - 129 grams of body fat/day, 595 - 903 grams bodyfat / week. Exercise will seriously accelerate this.

Lastly, a properly managed ketosis will reduce or eliminate hunger. The key is to eat ONLY until you are no longer hungry, not until you are full. This will gradually reduce the urge to eat. Most of the people I work with now have to remember to eat.