Why are apes skinny and humans fat?

Scientists studied dead humans and bonobos in an effort to understand why humans became the fat primate. What happened when chimps and humans diverged? It's not clear, but the results thousands of years later are.

...humans got fat. Chimps and bonobos are 13 percent skin, and we're only 6 percent skin, but we compensate for that by being up to 36 percent body fat on the high end of average, while bonobos average 4 percent. That's a wildly disproportional fatness differential.

From an interview of one of the authors of the paper.

So what happened on the path from common ancestor to Homo sapiens?
One of the things is, you've gotta shift the body around and change the muscle from the forelimbs if you're a quadrupedal ape. Our ancestors—and most apes—can venture into open areas, but they live in forests. They're really tied to having tree cover available, because they get hot.
So we developed fat so we could get away from forests?
Compared to the apes, we have less muscle, which is an energy savings, because it's such an expensive tissue. Two important things about the way we store fat: We store it around our buttocks and thighs, but you want to make sure that you're storing fat so it doesn't interfere with locomotion. You don't want it on your feet, for instance. So you concentrate it around the center of gravity. And you also don't want it to interfere with being able to get rid of heat.
What was the benefit of having fat down low and weak arms?
If you're moving away from the forest and tree cover, you want to be able to exploit food in a more mosaic habitat that has areas of bush and a few forests around rivers. You want to be able to move into a lot of different areas. So you've gotta get rid of your hair, and really ramp up those sweat glands. Our skin has really been reorganized for a lot of different functions.
Do chimps and bonobos not have sweat glands? 
They have sweat glands. They're not really functioning. All primates have eccrine sweat glands in their hands and feet. Monkeys have them on their chests. [But] they're not stimulated by heat.