Actually, what I have heard that is that out-of-shape, overweight people tend to be depressed. I think it has to do with the fact that they eat too much unhealthy carbs, and these carbs apparently make the brain secrete something, and it makes them depressed.
On OP:
You brought up a good point, because it reminds me of something I have always been saying. I feel that there should be a upper limit on how old a president can be. For example, let's say the POTUS cannot be older than, say, 55 or so. I think this makes sense, he is one of the most important people in the country, we can't have him die off during the middle of a huge armed conflict or something, it would just be bad. And this is not even talking about declining mental sharpness, mental confused brought on by advanced age...etc. We all know that as people get old, they become less healthy, less strong, less sharp versions of themselves. We don't want unhealthy, unfit, old people in the armed forces, why would we want them in the most important office in the world?