commonwealth n.

c. 1300, "belonging to all, owned or used jointly, general, of a public nature or character," from Old French comun "common, general, free, open, public" (9c., Modern French commun), from Latin communis "in common, public, shared by all or many; general, not specific; familiar, not pretentious." This is from a reconstructed PIE compound *ko-moin-i- "held in common," compound adjective formed from *ko- "together" + *moi-n-, suffixed form of root *mei- (1) "to change, go, move," hence literally "shared by all."

The second element of the compound also is the source of Latin munia "duties, public duties, functions," those related to munia "office." Perhaps reinforced in Old French by the Germanic form of PIE *ko-moin-i- (compare German gemein, Old English gemne "common, public, general, universal;" see mean (adj.)), which came to French via Frankish.

Used disparagingly of women and criminals since c. 1300. Meaning "pertaining equally to or proceeding equally from two or more" is from c. 1400. Meaning "usual, not exceptional, of frequent occurrence" is from late 14c. Sense of "not distinguished, belonging to the general mass" is from c. 1400; of things, "ordinary, not excellent," late 14c.

Common pleas is 13c., from Anglo-French communs plets, hearing civil actions by one subject against another as opposed to pleas of the crown. Common prayer is that done in public in unity with other worshipers; contrasted with private prayer. Common stock is attested from 1888. Common speech (late 14c.) is the vernacular, as opposed to Latin. Common good (late 14c.) translates Latin bonum publicum "the common weal." The college common room (1660s) is one to which all members have common access. 

mid-13c., "happiness," also "prosperity in abundance of possessions or riches," from Middle English wele "well-being" (see weal (n.1)) on analogy of health.