Middle English wei, "established road," from Old English weg (Mercian wæg) "track or path by which some place may be reached, line or course of travel, distance to be travelled."
This is reconstructed to be from Proto-Germanic *wega- "course of travel, way" (source also of Old Saxon, Dutch weg, Old Norse vegr, Old Frisian wei, Old High German weg, German Weg, Gothic wigs "way"). According to Watkins this is from PIE root *wegh- "to go, move, transport in a vehicle," also the source of voyage and wagon.
Other senses in Old English were "room, space, freedom of movement;" also, figuratively, "course of life" especially, in plural, ways, "habits of life" as regards moral, ethical, or spiritual choices. Also "method or manner of proceeding" (right way).
It is attested from mid-13c. as "place of passage, opening in a crowd." To make way "give room for passage" is from c. 1200. In nautical use, "progress through the water," by 1660s.
It is attested by c. 1300 as "manner in which something occurs" and by mid-15c. in reference to state or condition (in a bad way, family way). Phrase in the way of "in the matter or business of" is from 1630s. By way of "for the purpose of" is from 14c.
It is attested by 1590s as "course insisted upon," in get (or have) one's way (1590s), also have it (one's) way (1709). For there to be no two ways about it is by 1818.
Adverbial constructions this way "in this direction," that way "in that direction" are from late 15c. Out of the way "remote from society, not in the usual course" is by c. 1300. In the way "so placed or of such a nature as to impede" is from c. 1500.
From the "course of life" sense comes way of life (c. 1600). From the "course of travel" sense comes the figurative go separate ways (1837); one way or (the) other (1550s); have it both ways (1847); and the figurative sense of come a long way (1922).
To be by the way "along or near the road" was in Old English; figuratively, in discourse, by 1550s; introducing a new remark by 1610s.
To go out of one's way "do more than circumstances require" is by 1748. On my way, expressing intention to hurry and arrive quickly, is attested by 1919. In Middle English, by woods and ways was an alliterative way to say "everywhere."
Encouragement phrase way to go is short for that's the way to go. Adverbial phrase all the way "completely, to conclusion" is by 1915; the sexual sense is implied by 1924.
Ways and means "resources at a person's disposal" is attested from early 15c. (with means (n.)).