Thinner, or healthier?

This study showing a relationship between obesity and increased brain degeneration is interesting, but it more inclines me to further questioning than persuades me to adopt the new national pasttime of obsessing over weight. How could a longitudinal study such as this possibly tease apart causation and correlation between these two variables? It seems to me quite plausible that a brain in poor condition might predispose a person to become obese, since poor impulse control, planning skills, and cognitive ability would naturally make one less able to design and maintain a healthy, low-fat diet or regular exercise regimen. Furthermore, it's equally possible that both obesity and brain degeneration are products of a third, unidentified variable - high cholesterol consumption, lack of exercise, etc. Everyone knows people who eat like horses and don't get fat, as well as people who exercise regularly and eat healthy foods but remain heavyset, and it's pretty well established that metabolism rate and static body weight are strongly influenced by genetics. As such, focusing on making people thinner seems like it might be fighting the wrong battle - not to mention one that will be difficult to win. It's clear that being overweight is not a good sign in regards to health, but it's not necessarily clear that it (rather than related issues like diet or exercise regimen) is the critical risk factor it's made out to be. I wonder if public health officials ought not to focus their attention on related, more easily addressed lifestyle issues.