mid-14c., "to take possession of," also "to take up space or time, employ (someone)," irregularly borrowed from Old French occuper "occupy (a person or place), hold, seize" (13c.) or directly from Latin occupare "take over, seize, take into possession, possess, occupy," from ob "over" (see ob-) + intensive form of capere "to grasp, seize," from PIE root *kap- "to grasp." The final syllable of the English word is difficult to explain, but it is as old as the record; perhaps from a modification made in Anglo-French. During 16c.-17c. a common euphemism for "have sexual intercourse with" (sense attested from early 15c.), which caused it to fall from polite usage.
"A captaine? Gods light these villaines wil make the word as odious as the word occupy, which was an excellent good worde before it was il sorted." [Doll Tearsheet in "2 Henry IV"]Related: Occupied; occupying.