How can saturated fat and trans fat contribute to obesity?

Fat = calories: Fat is a very efficient way to intake calories which your body needs for energy, as well as a very efficient way to store energy. The problem occurs when calorie intake is greater than calorie usage. The body will then store the excess calories it as fat for future use as energy. Unfortunately with the widespread availabilty of food, that day may never come, and obesity subsequently develops.

Mostly a caloric: Phenomenon. Unfortunately fats are calorically dense. Twice as much as carbohydrates and proteins. So unfortuantely you don't have to eat too many fats(gram) wise before your intake of calories becomes so significant that you are consuming more calories than you are burning. In that setting you will start you store calories and usually in the form of fat.