c. 1200, gein, "advantage, benefit; help," c. 1300, "reward, profit, that which has been acquired" (possessions, resources, wealth), from Old French gain, gaaigne "gain, profit, advantage; work, business; booty; arable land" (12c.), from Germanic, and from Old Norse (see gain (v.)). Meaning "any incremental increase" (in weight, etc.) is by 1851. Related: Gains. The French word enfolded the notions of "profit from agriculture" and "booty, prey."
1520s, "obtain as profit," from French gagner, from Old French gaaignier "to earn, gain; trade; capture, win," also "work in the fields, cultivate land," from Frankish *waidanjan "hunt, forage," also "graze, pasture," from Proto-Germanic *waithanjan "to hunt, plunder," from *waithjo- "pursuit, hunting" (source also of Old English waþ "hunting," German Weide "pasture, pasturage," Old Norse veiðr "hunting, fishing, catch of fish").
This is from PIE root *weie- "to go after, strive after, pursue vigorously, desire," with noun derivatives indicating "force, power" (related to *wi-ro- "man;" see virile). Cognates include Sanskrit padavi- "track, path, trail," veti- "follows, strives, leads, drives;" Avestan vateiti "follows, hunts;" Greek hiemai "move oneself forward, strive, desire;" Lithuanian vyti "to chase, pursue;" Old Norse veiðr "chase, hunting, fishing;" Old English OE wað "a chase, hunt."
Meaning "obtain by effort or striving" is from 1540s; intransitive sense of "profit, make gain" is from 1570s. Meaning "arrive at" is from c. 1600. Of timepieces by 1861. Related: Gained; gaining. To gain on "advance nearer" is from 1719. To gain ground (1620s) was originally military.
1540s, "gain again, recover," as what has escaped or been lost, from French regaigner (Modern French regagner), from re- "again" (see re-) + gaginer, from Old French gaaignier "to earn, gain; trade; capture, win" (see gain (v.)). Meaning "arrive at again, return to" is from 1630s. Related: Regained; regaining.
The second element is obscure. Watkins suggests a suffixed form of the PIE root *weie- "to go after something, pursue with vigor" (see gain (v.)); de Vaan also traces it to a PIE form meaning "pursued." Meaning "the spoken or written form in which a person is invited" is from 1610s.