How do they determine "healthy" weight from confounding factors?

[ScienceNostalgia101]

In the United States, being "over"weight is associated with physical inactivity, and with the overeating of fast food, which happens to be high in saturated and trans fat.

 

So this leaves a question; when the medical community tries to determine what is supposedly the medically optimum weight based on age, height, etc... do they go by correlation or not? If not, what is their alternative to mere correlation, and if so, then how do they distinguish whether it is the weight that is causing those problems and not, let's say, the inactivity, the saturated fat, and the trans fat? If someone was physically active, but binged on unsaturated fats like avocado, fish, lentils, tofu, etc... to the point of being overweight, would they be healthier than the average "healthy" weight person? Would the weight itself do more good or harm, and on what grounds would they presume to know? (Not speaking as someone with weight issues; though ironically I used to be underweight with high cholesterol, so that might have sparked my skepticism on this matter.)