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c.1300, "to overthrow, destroy; to be overwhelmed; to harass," apparently from French, but Old French combrer "to seize hold of, lay hands on, grab, snatch, take by force, rape," has not quite the same sense. Perhaps a shortened formation from a verb akin to Middle English acombren "obstructing progress," from Old French encombrer, from combre "obstruction, barrier," from Vulgar Latin *comboros "that which is carried together," perhaps from a Gaulish word.
The likely roots are PIE *kom (see com-) + *bher- (1) "to bear" (see infer). Weakened sense of "to hamper, to obstruct or weigh down" is late 14c. Related: Cumbered; cumbering.