1832, "resembling brain matter;" 1845, "intelligent, clever," from brain (n.) + -y (2). Latin equivalent cerebrosus meant "passionate, enraged, hot-headed," leading Tucker to remark that " 'Brainy' is not a natural expression for 'frantic.' "
"soft, grayish mass filling the cranial cavity of a vertebrate," in the broadest sense, "organ of consciousness and the mind," Old English brægen "brain," from Proto-Germanic *bragnan (source also of Middle Low German bregen, Old Frisian and Dutch brein), of uncertain origin, perhaps from PIE root *mregh-m(n)o- "skull, brain" (source also of Greek brekhmos "front part of the skull, top of the head"). But Liberman writes that brain "has no established cognates outside West Germanic" and is not connected to the Greek word. More probably, he writes, its etymon is PIE *bhragno "something broken."
The custom of using the plural to refer to the substance (literal or figurative), as opposed to the organ, dates from 16c. Figurative sense of "intellectual power" is from late 14c.; meaning "a clever person" is first recorded 1914. To have something on the brain "be extremely eager for or interested in" is from 1862. Brain-fart "sudden loss of memory or train of thought; sudden inability to think logically" is by 1991 (brain-squirt is from 1650s as "feeble or abortive attempt at reasoning"). An Old English word for "head" was brægnloca, which might be translated as "brain locker." In Middle English, brainsick (Old English brægenseoc) meant "mad, addled."
adjective suffix, "full of or characterized by," from Old English -ig, from Proto-Germanic *-iga- (source also of Dutch, Danish, German -ig, Gothic -egs), from PIE -(i)ko-, adjectival suffix, cognate with elements in Greek -ikos, Latin -icus (see -ic). Originally added to nouns in Old English; used from 13c. with verbs, and by 15c. even with other adjectives (for example crispy).
<a href="https://www.etymonline.com/word/brainy">Etymology of brainy by etymonline</a>
Harper, D. (n.d.). Etymology of brainy. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/brainy