rest (n.1)

[sleep, repose, slumber] Old English ræste, reste "rest; a bed or couch; intermission of labor; mental peace, state of quiet or repose," from Proto-Germanic *rasto- (source also of Old Saxon resta "resting place, burial-place," Dutch rust, Old High German rasta, German Rast "rest, peace, repose"), a word of uncertain origin.

The original prehistoric signification of the Germanic noun was perhaps a measure of distance; compare Old High German rasta, which in addition to "rest" meant "league of miles," Old Norse rost "league, distance after which one rests," Gothic rasta "mile, stage of a journey." If so, perhaps a word from the nomadic period. But if the original sense was "repose," the sense was extended secondarily to "distance between two resting places."

Sense of "absence or cessation of motion" is from late 15c. The meaning "that on which anything leans for support, thing upon which something rests" is attested from 1580s, with specific senses developing later. In music, "an interval of silence," also the mark or sign denoting this, 1570s.

At rest "dead" is from mid-14c., on the notion of "last rest, the big sleep, the grave." The roadside rest stop for drivers on busy highways is by 1970. The colloquial expression give (something) a rest "stop talking about it" is by 1927, American English.

[R]est and repose apply especially to the suspended activity of the body ; ease and quiet to freedom from occupation or demands for activity, especially of the body ; tranquility and peace to the freedom of the mind from harassing cares or demands. [Century Dictionary]

"remainder, that which is left after a separation," early 15c., from French reste "remnant," from rester "to remain" (see rest (v.2)). Meaning "others, those not included in a proposition" is from 1530s.

[to repose; to cease from action] Middle English resten, from Old English ræstan, restan "take repose by lying down; lie in death or in the grave; cease from motion, work, or performance; be still or motionless; be undisturbed, be free from what disquiets; stand or lie as upon a support or basis," from Proto-Germanic *rastejanan (source also of Old Saxon restian, Old Frisian resta, Middle Dutch rasten, Dutch rusten, Old High German reston, German rasten, Swedish rasta, Danish raste "to rest"), a word of doubtful etymology (compare rest (n.1)).

Transitive senses "give repose to; lay or place, as on a support or basis" are from early 13c. Meaning "cease from, have intermission" is late 14c., also "rely on for support." In law, "voluntarily end the presentation of evidence to allow presentation of counter-evidence by the opposing party," by 1905. Related: Rested; resting.

To rest up "recover one's strength" is by 1895, American English. To rest in "remain confident or hopeful in" is by late 14c., biblical. Resting place "place safe from toil or danger" is from mid-14c.

Rest signifies primarily to cease from action or work, but naturally by extension to be refreshed by doing so, and further to be refreshed by sleeping. Repose does not necessarily imply previous work, but does imply quietness, and generally a reclining position, while we may rest in a standing position. [Century Dictionary]

[be left, remain] mid-15c., "remain, continue in existence," from Old French rester "to remain, stay" (12c.), from Latin restare "stand back, be left," from re- "back" (see re-) + stare "to stand" (from PIE root *sta- "to stand, make or be firm").

It has been largely confused and partly merged with rest (v.1), which, however, is Germanic.

The meaning "be in a certain state or position" (of affairs, etc.) is from late 15c.  The older sense of "to continue to be" is rare but in phrases such as rest assured. To rest with "be in the power of, depend upon" is by 1819.

The transitive sense of "to keep, cause to continue to remain" was common in 16c.-17c., "used with a predicate adjective following and qualifying the object" [Century Dictionary]. Hence the phrase rest you merry (1540s, Shakespeare also has rest you fair), earlier rest þe murie (mid-13c.), as a greeting, "rest well, be happy," from the old adverbial use of merry. The Christmas carol lyric God rest ye merry, gentlemen, often is mispunctuated.