Too much blind guessing. Here's the correct answer.
The error everyone makes in assuming that because it's bad for heart disease, it's bad for everything.
Obesity is a problem primarily because of cardiovascular reasons, like heart attack and stroke. Otherwise it's loaded with nutrition and calories. This probably explains why "overweight" (though not obese) are the longest-lived segment of society. Thinner people are running more on empty, leading to under-performing immune systems and healing.
That's where I'd start to look anyway.
And on top of all this, high fat content is known to help neurons function in cases with epilepsy, so again it's not a surprise here.