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1520s, from Anglo-French abeiance "suspension," also "expectation (especially in a lawsuit)," from Old French abeance "aspiration, desire," noun of condition of abeer "aspire after, gape" from à "at" (see ad-) + ba(y)er "be open," from Latin *batare "to yawn, gape" (see abash).
Originally in French a legal term, "condition of a person in expectation or hope of receiving property;" it turned around in English law to mean "condition of property temporarily without an owner" (1650s). Root baer is also the source of English bay (n.2) "recessed space," as in "bay window."