I don't think the first link really provides any real insight into the problem. First of all, the study isn't experimental. There could easily be many confounding variables here, such as depression causing more body satisfaction issues. Another issue could be that overweight people with low body satisfaction are less satisfied because they have been warned more about it (chicken-and-egg); for example, if a child had a binge eating disorder to begin with, their parents/doctors/friends would intervene more to try to stop them from gaining so much weight. The study also doesn't clearly define how the survey worked, and the study referenced for the survey didn't explain much either [1]. It doesn't seem like there's any measure of whether low body satisfaction means weight is too high/weight is too low (I think there's some nuance to this, for example someone desiring larger breasts may want to gain weight even if they see themselves as fat, and there's a big difference here based on culture). Finally, keep in mind the jump back to weight gain with "Very high body satisfaction". These are separated into 4 groups (apparently by quartile, although clearly every group is a different size just by looking at the chart), but this information could reveal a sharp spike as you get to the top 1% or something. Also, look at the difference in size between the 4 groups, the first is 4x larger than the last, which seems really strange.

[1] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3140795/#R27