For the context of the game, "Heavy means more elite" while light means cheaper and less effective.
There are many historical inaccuracies in this board game. The fun part is you don't have to follow exact history to make a good game. I was a history major, I realize there were no War elephants in 1800's due to cannons but there are in the game. just like you can buy samurai mercenaries, or build Big Ben in the Napoleonic Era and it was really finished in 1860. The fun part is you can create your own histories. Without getting too crazy naturally