Words related to be-
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.
It forms all or part of: abaft; about; alley (n.1) "open passage between buildings;" ambagious; ambassador; ambi-; ambidexterity; ambidextrous; ambience; ambient; ambiguous; ambit; ambition; ambitious; amble; ambulance; ambulant; ambulate; ambulation; ambulatory; amphi-; amphibian; Amphictyonic; amphisbaena; Amphiscians; amphitheater; amphora; amputate; amputation; ancillary; andante; anfractuous; be-; begin; beleaguer; between; bivouac; but; by; circumambulate; embassy; ember-days; funambulist; ombudsman; perambulate; perambulation; preamble; somnambulate; somnambulism; umlaut.
It is the hypothetical source of/evidence for its existence is provided by: Sanskrit abhitah "on both sides," abhi "toward, to;" Avestan aibi; Greek amphi "round about;" Latin ambi- "around, round about;" Gaulish ambi-, Old Irish imb- "round about, about;" Old Church Slavonic oba; Lithuanian abu "both;" Old English ymbe, German um "around."
Meaning "change from one state of existence to another" is from 12c. Older sense preserved in what has become of it? It drove out Old English weorðan "to befall." Meaning "to look well, suit or be suitable to" is early 14c., from earlier sense of "to agree with, be fitting or proper" (early 13c.).