> which is suggestive that there's probably something causal, in some direction, somewhere in there.

Perhaps suggestive, but far from conclusive (I know you know this too). To me, it is suggestive that there is likely some other factor that may explain the relationship better, but then again, I am wrong more often than right, so what do I know? ;)

For example, compare that to growing wealth inequality, and I wouldn't be surprised if that is a potential factor. Less income = less access to care, less access to healthier food options, perhaps less time to for self-care, etc., and if wealth/career potential is gatekept by academic achievement, economic utility, or intelligence, then I can see the two, intelligence and BMI, being correlated, but not directly causal. Though, no study would give people large sums of money to improve their lives, so I doubt we will know for certain.