Old English giefan (W. Saxon) "to give, bestow; allot, grant; commit, devote, entrust," class V strong verb (past tense geaf, past participle giefen), from Proto-Germanic *gebanan (cf. Old Frisian jeva, Middle Dutch gheven, Dutch geven, Old High German geban, German geben, Gothic giban), from PIE *ghabh- "to take, hold, have, give" (see habit). It became yiven in Middle English, but changed to guttural "g" by influence of Old Norse gefa "to give," Old Danish givæ. Meaning "to yield to pressure" is from 1570s.
Give in "yield" is from 1610s; give out is mid-14c., "publish, announce;" meaning "run out, break down" is from 1520s. Give up "surrender" is mid-12c. To give (someone) a cold seems to reflect the old belief that one could be cured of disease by deliberately infecting others. What gives? "what is happening?" is attested from 1940. Give-and-take (n.) is originally from horse racing (1769) and refers to races in which bigger horses were given more weight to carry, lighter ones less. General sense attested by 1778.