I can't think of anything worse than a diet based on fat. Other than some eskimos eating seals, I can't quite figure out whether there is some long term evidence of any benefit. There are certainly long term studies on the detrimental effects of animal fats, saturated fats and transfats.
I have never been fat myself, but I have been overweight by up to 2 stones and what really helped stabilise my weight have been cutting meat and reducing alcohol.
I don't know how each contributed individually, but I would say the alcohol reduction has been minor, as I have never been a heavy drinker, a case of going from 10 units a week down to 4 or 5 (couple of pints a week), whereas cutting meat has been a more significant change.
My meals are largely based on grains, pulses and vegetables. My protein intake would probably horrify most supporters of a "western diet", but I have seen no ill effect, if anything, I am stronger than I used to be.