bye n.

salutation in parting, also goodbye, good bye, good-by, 1590s, from godbwye (1570s), a contraction of God be with ye (late 14c.), influenced by good-day, good evening, etc. As a noun from 1570s. Intermediate forms in 16c. include God be wy you, God b'uy, God buoye, God buy, etc.

"soothing song sung to infants," 1580s, noun use of the words lulley by (1560s), from Middle English lollai or lullay, a common burden in nursery songs, from lullen (see lull (v.)). Second element perhaps from by in good-bye or simply a meaningless extension.

Old English be- (unstressed) or bi (stressed) "near, in, by, during, about," from Proto-Germanic *bi "around, about," in compounds often merely intensive (source also of Old Saxon and Old Frisian bi "by, near," Middle Dutch bie, Dutch bij, German bei "by, at, near," Gothic bi "about"), from PIE *bhi, reduced form of root *ambhi- "around."

As an adverb by c. 1300, "near, close at hand."

OED (2nd ed. print) has 38 distinct definitions of it as a preposition. Originally an adverbial particle of place, which sense survives in place names (Whitby, Grimsby, etc., also compare rudesby). Elliptical use for "secondary course" was in Old English (opposed to main, as in byway, also compare by-blow "illegitimate child," 1590s, Middle English loteby "a concubine," from obsolete lote "to lurk, lie hidden"). This also is the sense of the second by in the phrase by the by (1610s).

By the way literally means "along the way" (c. 1200), hence "in passing by," used figuratively to introduce a tangential observation ("incidentally") by 1540s. To swear by something or someone is in Old English, perhaps originally "in the presence of." Phrase by and by (early 14c.) originally meant "one by one," with by apparently denoting succession; modern sense of "before long" is from 1520s.

By and large "in all its length and breadth" (1660s) originally was nautical, "sailing to the wind and off it," hence "in one direction then another;" from nautical expression large wind, one that crosses the ship's line in a favorable direction.