"Action of hardening," 1837; also "manner or position in which something is set" (1530s), hence "general movement, direction, tendency" (1560s); "build, form" (1610s), hence "bearing, carriage" (1855); "action of fixing the hair in a particular style" (1933).
"Something that has been set" (1510s), hence the use in tennis (1570s) and the theatrical meaning "scenery for an individual scene in a play, etc.," recorded from 1859. Other meanings OED groups under "miscellaneous technical senses" include "piece of electrical apparatus" (1891, first in telegraphy); "burrow of a badger" (1898). Old English had set "seat," in plural "camp; stable," but OED finds it "doubtful whether this survived beyond OE." Compare set (n.1).
Set (n.1) and set (n.2) are not always distinguished in dictionaries; OED has them as two entries, Century Dictionary as one. The difference of opinion seems to be whether the set meaning "group, grouping" (here (n.2)) is a borrowing of the unrelated French word that sounds like the native English one, or a borrowing of the sense only, which was absorbed into the English word.
Old English settan (transitive) "cause to sit, put in some place, fix firmly; build, found; appoint, assign," from Proto-Germanic *(bi)satejanan "to cause to sit, set" (source also of Old Norse setja, Swedish sätta, Old Saxon settian, Old Frisian setta, Dutch zetten, German setzen, Gothic satjan), causative form of PIE *sod-, a variant of root *sed- (1) "to sit." Also see set (n.2).
The intransitive sense from c. 1200, "be seated." The word was used in many disparate senses by Middle English; sense of "make or cause to do, act, or be; start" and that of "mount a gemstone" attested by mid-13c. Confused with sit since early 14c. Of the sun, moon, etc., "to go down," recorded from c. 1300, perhaps from similar use of the cognates in Scandinavian languages. To set (something) on "incite to attack" (c. 1300) originally was in reference to hounds and game.
Meaning "complete collection of pieces" is from 1680s. Meaning "group of pieces musicians perform at a club during 45 minutes" (more or less) is from c. 1925, though it is found in a similar sense in 1580s. Set piece is from 1846 as "grouping of people in a work of visual art;" from 1932 in reference to literary works.
Old English up, uppe, from Proto-Germanic *upp- "up" (source also of Old Frisian, Old Saxon up "up, upward," Old Norse upp; Danish, Dutch op; Old High German uf, German auf "up"; Gothic iup "up, upward," uf "on, upon, under;" Old High German oba, German ob "over, above, on, upon"), from PIE root *upo "under," also "up from under," hence also "over."
As a preposition, "to a higher place" from c. 1500; also "along, through" (1510s), "toward" (1590s). Often used elliptically for go up, come up, rise up, etc. Up the river "in jail" first recorded 1891, originally in reference to Sing Sing, which is up the Hudson from New York City. To drive someone up the wall (1951) is from the notion of the behavior of lunatics or caged animals. Insulting retort up yours (scil. ass) is attested by late 19c.