Old English heall "spacious roofed residence, house; temple; law-court," any large place covered by a roof, from Proto-Germanic *hallo "covered place, hall" (source also of Old Saxon, Old High German halla, German halle, Dutch hal, Old Norse höll "hall;" Old English hell, Gothic halja "hell"), from PIE root *kel- (1) "to cover, conceal, save."
Sense of "passageway in a building" evolved 17c., from the time when the doors to private rooms opened onto the large public room of the house. Older sense preserved in town hall, music hall, etc., in use of the word in Britain and Southern U.S. for "manor house," also "main building of a college" (late 14c.). French halle, Italian alla are from Middle High German. Hall of fame attested by 1786 as an abstract concept; in sporting sense first attested 1901, in reference to Columbia College; the Baseball Hall of Fame opened in 1939. Related: Hall-of-famer.
way n.
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 *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"), from PIE root *wegh- "to go, move, transport in a vehicle."
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 (1847); and the figurative sense of come a long way (1922).
Adverbial phrase all the way "completely, to conclusion" is by 1915; sexual sense implied by 1924. Make way is from c. 1200. Ways and means "resources at a person's disposal" is attested from early 15c. (with mean (n.)). Way out "means of exit" is from 1926. Encouragement phrase way to go is short for that's the way to go.