Despite this, we still tend to associate body types with levels of (un)productivity.

You know why? Because people who are morbidly obese really can be less productive than someone who is in shape, or only mildly overweight. At certain points of weight, it becomes very difficult, if not impossible, to do some tasks. You won't get up and around as much. Your weight may require special accommodations (such as a chair built to take three or more normal people). Sometimes, basic hygiene becomes a challenge.

I had a co-worker in the past who went from 280 to about 500 or more pounds because he just could not stop eating. When his wife left him, his depression caused him to eat even more (been there myself). The office had to order two special chairs for him because he broke the first one.

It took him forever to walk to the elevator to go from the first to the second floor. He was always asking us to run things for him because he was "too tired." He eventually quit and went on disability, but not before he got several 'talking-tos' about expecting everyone else to do his work for him.