Some weapons are dealing the same amount of damage regardless of their size. For instance, the starting daggers of assassins all do 1d4 damage whether they are small, medium, or large. I also found a large broadsword which dealt 1d7 damage (same as medium; did 2d10 in earlier versions), and a large morningstar which dealt 1d5/1d5 damage (same as medium; did 2d7/2d7 in earlier versions).