Did they control for efforts to change you body? Most fat people are trying to be thinner. Plenty of ways that people are told to change their body involve extreme stress to your body (caloric restriction, extreme diets, stimulant pills).
Did you know that being underweight is ALSO associated with health problems, sometimes as extreme as the ones associated with being very fat.
Anybody reading this and wanting a more nuanced understanding of this stuff should listen to the first few episodes of the podcast Maintenance Phase https://www.maintenancephase.com/
edit: I'm getting downvoted for pointing out two well documented factors that the linked article doesn't seem to account for - I thought we believed in facts and rationality here?