way (n.) Look up way at Dictionary.com
Old English weg "road, path; course of travel; room, space, freedom of movement;" also, figuratively, "course of life" especially, in plural, "habits of life" as regards moral, ethical, or spiritual choices, from Proto-Germanic *wegaz (cognates: Old Saxon, Dutch weg, Old Norse vegr, Old Frisian wei, Old High German weg, German Weg, Gothic wigs "way"), from PIE *wegh- "to move" (see weigh).

From c.1300 as "manner in which something occurs." Adverbial constructions attested since Middle English include this way "in this direction," that way "in that direction," both from late 15c.; out of the way "remote" (c.1300). In the way "so placed as to impede" is from 1560s.

From the "course of life" sense comes way of life (c.1600), get (or have) one's way (1590s), have it (one's) way (1709). From the "course of travel" sense comes the figurative go separate ways (1837); one way or (the) other (1550s); have it both ways (1914); and the figurative sense of come a long way (1922).

Adverbial phrase all the way "completely, to conclusion" is by 1915; sexuial sense implied by 1924. Make way is from c.1200. Ways and means "resources at a person's disposal" is attested from early 15c. Way out "means of exit" is from 1926. Encouragement phrase way to go is short for that's the way to go.
way (adv.) Look up way at Dictionary.com
c.1200, short for away (adv.). Many expressions involving this are modern and American English colloquial, such as way-out "far off;" way back "a long time ago" (1887); way off "quite wrong" (1892). Any or all of these might have led to the slang adverbial meaning "very, extremely," attested by 1984 (as in way cool).