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1590s, "to run off," probably a reborrowing from Middle Dutch (ont)lopen "run away." Sense of "run from parents to marry secretly" is 19c. Anglo-French aloper "run away from a husband with one's lover" is attested from mid-14c., but there is a gap of many years.
The Anglo-French word represents Old French es- + Middle English lepen "run, leap" (see leap (v.)).
The oldest Germanic word for "wedding" is represented by Old English brydlop (cf. Old High German bruthlauft, Old Norse bruðhlaup), literally "bride run," the conducting of the woman to her new home. Related: Eloped; eloping.