I have several that show fat reduces cognitive ability, reduces memory, breaks the blood/brain barrier, and is correlated with and lowers IQ. I do not think I have anything that explicitly states being fat will make you literally mentally ill, but it is fairly evident that it practically does. As far as the other way around, being fat is linked to inherent poor impulse control and different satiety signals, which again, is not an actual mental illness, but also again, in practice it is not a high functioning person. Sarcasm aside, I do generally feel unsafe sometimes around people who so clearly do not think straight. All it takes it for them to throw a tantrum, for example, and they will run me over with their car. Even if they are not able to be diagnosed as sick, just plain stupid can be every bit as dangerous as actively insane.