Fat parents often have fat children. There’s a strong correlation.

yes, that is true, and we know several reasons for it, but it is irrelevant both to the narrow issue of whether fat cells produced in childhood derange your caloric intake regulatory homeostasis thereafter, and to the broader issue of why there's an obesity pandemic

It certainly was rarer but this was a known phenomenon occurring at least back in the 1960s

Off the top of my head I know there’s a speech of JFKs where he advocates for child health saying quote “there’s nothing more unfortunate than fat chubby children”