The undeleted comments in this thread and the other two threads cited by /u/caffarelli, as well as my own research, suggest that there is no evidence that people were smoking marijuana in colonial America. While hemp was a popular crop in the Chesapeake, and later Kentucky, it was only used to make rope and bagging. A History of the Hemp Industry in Kentucky by James Hopkins has nothing to say about marijuana as a drug until the 1940s. I really think we need to work backwards with this topic; if I might suggest a more fruitful question, "What are the origins of marijuana smoking in America?" Bonus points for a global perspective.

Previous answers that may be of interest:

• How frequently did Jefferson and Washington smoke cannabis? (if at all)

• Did Native Americans smoke marijuana?

If we are unsure of marijuana usage in colonial America, was it being used in any form in Europe at that time?