late 14c., "to hold, occupy, reside in" (without regard to ownership), a back formation from possession and in part from Old French possesser "to have and hold, take, be in possession of" (mid-13c.), from Latin possess-, past participle stem of possidere "to have and hold, hold in one's control, be master of, own," probably a compound of potis "having power, powerful, able" (from PIE root *poti- "powerful; lord") + sedere, from PIE root *sed- (1) "to sit."
According to Buck, Latin possidere was a legal term first used in connection with real estate. Meaning "to hold as property" in English is recorded from c. 1500. Demonic sense is recorded from 1530s (implied in possessed). Related: Possessed; possessing. The other usual Latin verb for "to possess," tenere, originally was "to hold," then "occupy, possess" (see tenet).