From what i've read, ive taken a few points:

fatty food does not cause or contribute to obesity. Total intake does.

1000 excess calories of fat and 1000 excess calories of sugar will roughly cause the same weight increase.

1000 calories of fat is far more satiating than 1000 calories of sugar and therefore leads to lower future consumption of calories. 1000 calories of the former may take 4 hrs to become hungry, whereas 1000 calories of the latter may take 1 hour to become hungry, for example.

Saturated fats a no more correlated with heart disease than other forms of fats.

Some of the science is linked here: http://www.dietdoctor.com/science