how and why societies over a period of centuries across different countries went from a "rich people == fat == good" to a "rich people == thin == good" equation            Except that  "rich people == fat == good"  equation never existed.  It's a newfangled fabrication.   In times of scarce food supply of course there were more fats among the lesser poor / rich than among the poor, but fat was NEVER seen as  a  value or virtue,  bar a small handful of societies / tribes.