late 14c., pensioun, "payment for services," especially "a regular reward or annual payment out of a will or benefice" (early 14c., in Anglo-Latin), from Old French pension "payment, rent" (13c.) and directly from Latin pensionem (nominative pensio) "a payment, installment, rent," from past-participle stem of pendere "to hang, cause to hang; weigh; pay" (from PIE root *(s)pen- "to draw, stretch, spin"). For the financial sense of the Latin verb, see pound (n.1).
Meaning "regular payment to a person in consideration of past service" is from 1520s, hence "periodic payment made to a person retired from service on account of age or disability" (originally especially government pay to soldiers and sailors). Meaning "boarding house, boarding school" is attested from 1640s, from a sense in French based on the meaning "money paid for board," and in English it is usually in reference to places in France or elsewhere on the Continent.
1640s, "to live in a pension," from pension (n.) or else from French pensionner. Meaning "to grant a pension" is from 1702. Related: Pensioned; pensioning.