by c. 1200 as an emphatic form of Old English of (see of), employed in the adverbial use of that word. The prepositional meaning "away from" and the adjectival sense of "farther" were not firmly fixed in this variant until 17c., but once they were they left the original of with the transferred and weakened senses of the word. Meaning "not working" is from 1861.
Off the cuff "extemporaneously, without preparation" (1938) is from the notion of speaking from notes written in haste on one's shirt cuffs. In reference to clothing, off the rack (adj.) "not tailored, not made to individual requirements, ready-made" is by 1963, on the notion of buying it from the rack of a clothing store; off the record "not to be publicly disclosed" is from 1933; off the wall "crazy" is 1968, probably from the notion of a lunatic "bouncing off the walls" or else in reference to carom shots in squash, handball, etc.
"member of a criminal gang practicing extortion, 'protection,' intimidation, etc.," 1927, a word from Prohibition, from racket (n.1) in the "dishonest activity" sense + -eer. Earlier (1926) in reference to organizers of fraudulent bankruptcies. By 1928 as a verb. Related: Racketeering, verbal noun (1927).
[A] racketeer is nothing more nor less than a gangster who has organized thuggery along business lines. ["What is a Racketeer?" Brooklyn Daily Eagle, Oct. 7, 1928]
Meaning "sustaining parts of a structure fitted together" is from c. 1400. Meaning "enclosing border" of any kind is from c. 1600; specifically "border or case for a picture or pane of glass" from 1660s. The meaning "human body" is from 1590s. Of bicycles, from 1871; of motor cars, from 1900. Meaning "separate picture in a series from a film" is from 1916. From 1660s in the meaning "particular state" (as in Frame of mind, 1711). Frame of reference is 1897, from mechanics and graphing; the figurative sense is attested from 1924.
Middle English rēchen, from Old English ræcan, reccan "to reach out, stretch or extend outward, hold forth, extend in continuity or scope," also "to succeed in touching, succeed in striking;" also "to address, speak to," also "to offer, present, give, grant."
This is proposed to be from Proto-West Germanic *raikejanan "stretch out the hand" (source also of Old Frisian reka "to give, pay," Middle Dutch reken, reiken, Old High German reihhen, reichen "give, reach out, get," Dutch reiken, German reichen "to reach, to pass, to hand, to give; to be sufficient"), from Proto-Germanic *raikijanau, which is probably from PIE root *reig- "to stretch, stretch out, be stretched; be stiff."
Sometimes 16c. spelled retch. As "to hand (someone something), give" from c. 1300. The meaning "arrive at, succeed in getting to" is early 14c.; that of "succeed in influencing" is from 1660s. Related: Reached; reaching. Shakespeare uses the now-obsolete past tense form raught (Old English ræhte).
Colloquial reach-me-down "ready-made" (of clothes) is recorded from 1862, from notion of being on the rack in a finished state.