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1590s, "to assign quarters to," earlier, as a noun, "official record or register" (Middle English), from Anglo-French billette "list, schedule," diminutive of bille (see bill (n.1)). Related: Billeted; billeting.
thick stick of wood, mid-15c., from Middle French billette, diminutive of bille "stick of wood" (see billiards).
"document, note;" see billet-doux.