Middle English (originally in the sense 'pay a debt, discharge a liability'): from Old French acquiter, from medieval Latin acquitare 'pay a debt', from ad- 'to' + quitare 'set free'.

• quit from Middle English:

  An Old French word from the same root as quiet, Latin quietus ‘quiet, still, resting’. The first meanings of quit were ‘to pay off a debt’, ‘to repay a service or favour’, and ‘to set free’. It also meant ‘to declare a person not guilty’, a meaning for which we would now use the related word acquit. The modern meanings, ‘to leave, go away’, and ‘to stop doing something’, are from the 17th century. To call it quits is to agree that terms are now equal, especially in the settlement of a debt, or to decide to abandon what you are doing in order to cut your losses. It dates back only to the 1890s and is a fairly informal expression, but an earlier version, cry quits, is recorded from the 1630s and comes from the world of officialdom. Church records of accounts from the late 15th century use the word quits to indicate that money owing to someone has been paid in full. Church business was usually conducted in Latin, and so quits probably arose from a scribe's shortening of the medieval Latin word quittus, meaning ‘discharged’, written on receipts to indicate that the goods had been paid for. Quite, found from the Middle Ages in the sense ‘completely, fully’ is probably from quit. The sense ‘fairly’ does not develop until the 19th century.