Entries linking to by-path
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.
Old English paþ, pæþ "narrow passageway or route across land, a track worn by the feet of people or animals treading it," from West Germanic *patha- (source also of Old Frisian path, Middle Dutch pat, Dutch pad, Old High German pfad, German Pfad "path"), a word of uncertain origin, not attested in Old Norse or Gothic.
The original initial -p- in a Germanic word is an etymological puzzle. Don Ringe ("From Proto-Indo-European to Proto-Germanic," Oxford 2006), reflecting an old theory, describes it as "An obvious loan from Iranian ..., clearly borrowed after Grimm's Law had run its course." Watkins says the word is "probably borrowed (? via Scythian) from Iranian *path-," from PIE root *pent- "to tread, go, pass" (source of Avestan patha "way;" see find (v.)), but this is too much of a stretch for OED and others. In Scotland and Northern England, commonly a steep ascent of a hill or in a road.