"to attack persistently, worry, pester," 1790, from badger (n.), based on the behavior of the dogs in the medieval sport of badger-baiting, still practiced in late 19c. England as an attraction to low public houses. Related: Badgered; badgering.

A badger is put into a barrel, and one or more dogs are put in to drag him out. When this is effected he is returned to his barrel, to be similarly assailed by a fresh set of dogs. The badger usually makes a most determined and savage resistance. [Century Dictionary]