Avocado doesn't specifically make you fat (nor does any other food); eating more calories than you burn in a given day makes you gain weight.
Avocado is, does, however, have both a high density of nutrients and calories relative to portion sizes. For most meals (where Avocado is a component of the meal), a quarter to a half (at most) of an avocado is all the calories most of us can spare without risk of weight gain.
Yes avocado is a fatty food. It is made of monounsaturated fat, which is 63 percent and polyunsaturated fats ( 20 percent). It doesn't need to be cooked. Compared to meats it has same amount of fats in it.