Fat doesn't make you fat. Overeating is generally the problem. Check out a book called The Big Fat Surprise -- it's quite a good read.

Because from a weight-loss perspective it doesn't matter what you eat, only how much calories you stuff into your mouth. You could eat nothing but bacon and still lose weight, if you eat only so much that you still burn more calories per day than the bacon delivers. If you keep your portions the same size but move to food with more calories, you will of course gain weight.

Fat can also trigger parts of your system to stop craving it, so you stop trying to aquire it by overeating. There are some science articles about it.

Staving off constant hunger can be as easy as cooking up a lentil (daal) soup that has some oil/butter in it. The lentils make you get a very full satisfied feeling in the bowel and the fats hit the part that wants fats.

Carbs are processed first, so if you don't eat carbs, in theory your body will burn depot fat earlier.

You still need to eat less calories than you burn though.