c. 1200, from Old English æmettig, of persons, "at leisure, not occupied; unmarried" (senses now obsolete), also, of receptacles, "containing nothing," of places, "unoccupied," from æmetta "leisure."
Watkins explains it as from Proto-Germanic *e-mot-ja-, with a prefix of uncertain meaning + Germanic *mot- "ability, leisure," possibly from PIE root *med- "take appropriate measures." A sense evolution from "at leisure" to "containing nothing, unoccupied" is found in several languages, such as 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 -p- is a euphonic insertion. Of words, etc., "destitute of force or effect," mid-14c. Related: Emptier. The figurative sense of empty-nester is attested by 1960.