From how I'm reading this, couldn't this easily be something like: unhealthy foods tend to have PFAS, so people who eat unhealthy food and gain weight also might have an increase in their blood, but this is just a correlation not a causation
I don't know why you're getting downvoted. I read the methods section and the stats model doesn't seem to adjust for "calories consumed after dieting stopped". Those calories, as you point out, can be correlated with PFAS because of their association with high-calorie foods. This seems to me like a potential confounding factor.
it'd be interesting to know if the PFAs affected the caloric equation (greater absorption, thermic effect of digestion, NEAT), if it affected behavior (maybe PFAs stimulate appetite?), or if it's simply association with foods which have known Caloric/Behavior effects ... (eg processed foods have lower satiation often leading to a behavior of eating more calories)
Even "whole" ingredients are often packaged in plastics. I think there's a lot going on, not to mention breaking free of metabolic dysfunction is extremely difficult for a lot of reasons.
In either case, an intentionally low PFAS diet would result in weight loss, as it would necessitate removal of those unhealthy foods.