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.
road n.
Middle English rode, from Old English rad "riding expedition, journey, hostile incursion," from Proto-Germanic *raido (source also of Old Frisian red "ride," Old Saxon reda, Middle Dutch rede, Old High German reita "foray, raid"), from PIE *reidh- "to ride" (see ride (v.)). Also related to raid (n.).
In Middle English it was still, "a riding, a journey on horseback; a mounted raid;" the sense of "an open passage or way for traveling between two places" is recorded from 1590s, and the older senses now are obsolete. "The late appearance of this sense makes its development from sense 1 somewhat obscure," according to OED, which however finds similar evolutions in Flemish and Frisian words. The modern spelling was established 18c.
The meaning "narrow stretch of sheltered water near shore where ships can lie at anchor" is from early 14c. (as in Virginia's Hampton Roads). In late 19c. U.S. use it is often short for railroad.
On the road "traveling" is from 1640s. Road test (n.) of a vehicle's performance is by 1906; as a verb from 1937. Road hog "one who is objectionable on the road" [OED] is attested from 1886; road rage is by 1988. Road map is from 1786; road trip is by 1950, originally of baseball teams. Old English had radwerig "weary of traveling."