"to strike repeatedly" (with something), c. 1500, a word of unknown origin; according to one old theory it is perhaps from early 13c. pelten "to strike," a variant of pilten "to thrust, strike," from an unrecorded Old English *pyltan, from Medieval Latin *pultiare, from Latin pultare "to beat, knock, strike," or [Watkins] pellere "to push, drive, strike" (from PIE root *pel- (5) "to thrust, strike, drive"). OED doubts this. Or it might be from Old French peloter "to strike with a ball," from pelote "ball" (see pellet (n.)) [Klein].
From 1680s as "to go on throwing (missiles) with intent to strike." The meaning "proceed rapidly and without intermission" (1831) is from the notion of beating the ground with rapid steps. Related: Pelted; pelting.