My favorite show is based on the 2nd/3rd century in China. They fed their armies with rice primarily. They didn't have ham planets going up against each other like sumo wrestlers. Their populations weren't fat either. In the past most often the fat fucks were rich people. There was a rich warlord called Dong Zhuo. The rich were able to consume more meat, which is known to make you bigger (see Daniel chapter 1 in the Bible). I wouldn't be surprised to find them consuming more alcohol and sweet fruits as well. It is probably the fat in meat that contributes to being bigger since protein is not a good energy source.