Aye
late 16th century: probably from I, first person personal pronoun, expressing assent.
wiktionary
From Middle English aye, ai, aȝȝ, from Old Norse ei, ey, from Proto-Germanic *aiwa, *aiwō(“ever, always”) (compare Old English āwo, āwa, ā, ō, Middle Dutch ie, German je), from *aiwaz(“age; law”) (compare Old English ǣ(w)(“law”), West Frisian ieu(“century”), Dutch eeuw(“century”)), from Proto-Indo-European *h₂eyu-(“long time”) (compare Irish aois(“age, period”), Breton oad(“age, period”), Latin ævum(“eternity”), Ancient Greek αἰών(aiṓn)). Doublet of aevum.
"Appears suddenly about 1575, and is exceedingly common about 1600." [1] Probably from use of aye(“ever, always”) as expression of agreement or affirmation, or from Middle English a ye(“oh yes”), or synthesis of both. More at oh, yea.
Probably of multiple motivations, the sounds having been chosen for functional reasons.
etymonline
aye (interj.)
word of assent to a question, 1570s, of unknown origin; perhaps a variant of I, meaning "I assent;" or an alteration of Middle English yai "yes" (see yea); or from aye (adv.) "always, ever."
aye (adv.)
"always, ever," c. 1200, from Old Norse ei "ever" (cognate with Old English a "always, ever"), from Proto-Germanic *aiwi-, extended form of PIE root *aiw- "vital force, life; long life, eternity" (source also of Greek aiōn "age, eternity," Latin aevum "space of time").
