What do you mean when it became "too heavy to carry around"? Did the amount of gold required to purchase a specific item increase over time? If it wasn't too heavy to carry around for 2600 years, what changed at that point in time?
My thinking would lead me to believe that printing presses were not commonly available before the 1600s or so, which would have prevented paper money from being feasible. Again, just thinking aloud here, and curious as to what history/facts support the "too heavy to carry around" argument.