The story
From prepossess + -ing. Attested in 1610s with the meaning of "getting possession of (ground or land) beforehand". The meaning "to possess (a person) beforehand with a feeling, notion, etc." developed in 1630s, acquiring by the 40s of the same century the meaning of "to cause (someone) to have a favorable opinion of something, preoccupy the mind or heart of".
Etymology from Wiktionary, CC BY-SA 4.0.