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c.1200, from Old English æmettig "at leisure, not occupied, unmarried," from æmetta "leisure," from æ "not" + -metta, from motan "to have" (see might (n.)). The -p- is a euphonic insertion.
Sense evolution from "at leisure" to "empty" is paralleled in several languages, e.g. Modern Greek adeios "empty," originally "freedom from fear," from deios "fear." "The adj. adeios must have been applied first to persons who enjoyed freedom from duties, leisure, and so were unoccupied, whence it was extended to objects that were unoccupied" [Buck].
The adjective also yielded a verb (1520s), replacing Middle English empten, from Old English geæmtigian. Related: Emptied; emptying. Figurative sense of empty-nester first attested 1987. Empty-handed attested from 1610s.