1590s, "act of taking away entirely;" see remove (v.) + -al (2). From 1640s specifically as "dismissal from an office or a post," also "act of changing one's habitation." Also occasionally a quasi-euphemism for "murder." The earlier noun was remove (n.); also removing, remeving (late 14c.).

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.

as a modifier, "done from a moving vehicle," by 1989 (originally of shootings), from the verbal phrase; see drive (v.) + by (prep.).

1640s, "an evasion, a leaving behind by artifice," from verbal phrase; see go (v.) + by (adv.). From 1650s as "a passing without notice, intentional disregard." Compare bygone.

late 14c., "secondary name;" 1570s, "nickname," from by + name (n.).

also byproduct, "secondary or additional product;" 1849, from by + product.

also passerby, 1560s, from agent noun of pass (v.) + by; earlier, this sense was in passager (see passenger).

also standby, 1796, "that which stands by one," originally nautical, of a vessel kept nearby for emergencies, from verbal phrase stand by "await, support, remain beside" (mid-13c.); see stand (v.) + by. Meaning "state of being ready for duty" is from 1946. In civil aviation, as an adjective meaning "without a booked ticket," from 1961. As an order to hold one's self in readiness, it is recorded from 1660s.

"side road," late 14c., from by + path.

"side road," 1670s, from by + road.