The practice seems to have come from the Etruscans (although the Etruscan men ate in the same room at the same time as their wives, unlike the Republic-era Romans and the Greeks). Boogieman’s suggestion that it started centuries earlier among nomadic ancestors looks pretty plausible to me.
I would lose a lot of weight because I would have more food on me than in me.
Do you suppose they could have had some notion that it was more helpful for the digestion to be in such a position?