Middle English kēpen, from late Old English cepan (past tense cepte) "to seize, hold; seek after, desire," also "to observe or carry out in practice; look out for, regard, pay attention to," from Proto-Germanic *kopjan, which is of uncertain origin. Old English cepan was used c. 1000 to render Latin observare, so perhaps it is related to Old English capian "to look" (from Proto-Germanic *kap-), which would make the basic sense "to keep an eye on, see to it."
The word prob. belonged primarily to the vulgar and non-literary stratum of the language; but it comes up suddenly into literary use c. 1000, and that in many senses, indicating considerable previous development. [OED]
The senses exploded in Middle English: "to guard, defend" (12c.); "restrain (someone) from doing something" (early 13c.); "take care of, look after; protect or preserve (someone or something) from harm, damage, etc." (mid-13c.); "preserve, maintain, carry on" a shop, store, etc. (mid-14c.); "prevent from entering or leaving, force to remain or stay" (late 14c.); "preserve (something) without loss or change," also "not divulge" a secret, private information, etc., also "to last without spoiling" (late 14c.); "continue on" (a course, road, etc.), "adhere to" a course of action (late 14c.); "stay or remain" (early 15c.); "to continue" (doing something) (mid-15c.). It is used to translate both Latin conservare "preserve, keep safe" and tenere "to keep, retain."
From 1540s as "maintain for ready use;" 1706 as "have habitually in stock for sale." Meaning "financially support and privately control" (usually in reference to mistresses) is from 1540s; meaning "maintain in proper order" (of books, accounts) is from 1550s.
To keep at "work persistently" is from 1825; to keep on "continue, persist" is from 1580s. To keep up is from 1630s as "continue alongside, proceed in pace with," 1660s as "maintain in good order or condition, retain, preserve," 1680s as "support, hold in an existing state." To keep it up "continue (something) vigorously" is from 1752. To keep to "restrict (oneself) to" is from 1711. To keep off (trans.) "hinder from approach or attack" is from 1540s; to keep out (trans.) "prevent from entering" is from early 15c.
mid-13c., "care or heed in watching," from keep (v.). Meaning "innermost stronghold or central tower of a castle" is from 1580s; OED says this is perhaps a translation of Italian tenazza, the notion being "that which keeps" (someone or something). The sense of "food required to keep a person or animal" is attested from 1801 (to earn (one's) keep is from 1885). For keeps "completely, for good" is American English colloquial, from 1861, probably from the notion of keeping one's winnings in games such as marbles.
mid-15c., "to keep something back, hinder," from back (adv.). The meaning "cause to move back" is from 1781. The intransitive sense of "move or go back" is from late 15c. The meaning "furnish with a back or backing" is from 1728, from back (n.). The meaning "to support" (as by a bet) is attested from 1540s. Related: Backed; backing.
"being behind, away from the front, in a backward direction," Middle English, from back (n.) and back (adv.); it is often difficult to distinguish from these when the word is used in combinations. Formerly with comparative backer (c. 1400), also backermore. To be on the back burner in the figurative sense of "postponed" is by 1960, from the image of a cook keeping a pot there to simmer while at work on another concoction at the front of the stove.
"to or toward the rear or the original starting place; in the past; behind in position," literally or figuratively, late 14c., shortened from abak, from Old English on bæc "backwards, behind, aback" (see back (n.), and compare aback). To give (something) back is to give it again, to give it in the opposite direction to that in which it was formerly given. Adverbial phrase back and forth is attested by 1814.
Old English bæc "back," from Proto-Germanic *bakam (cognates: Old Saxon and Middle Dutch bak, Old Frisian bek), with no known connections outside Germanic. In other modern Germanic languages the cognates mostly have been ousted in this sense by words akin to Modern English ridge (such as Danish ryg, German Rücken).
Many Indo-European languages show signs of once having distinguished the horizontal back of an animal (or a mountain range) from the upright back of a human. In other cases, a modern word for "back" may come from a word related to "spine" (Italian schiena, Russian spina) or "shoulder, shoulder blade" (Spanish espalda, Polish plecy).
By synecdoche, "the whole body," especially with reference to clothing. The meaning "upright part of a chair" is from 1520s. As a U.S. football position by 1876, so called from being behind the line of rushers; further distinguished according to relative position as quarterback, halfback, fullback. To turn (one's) back on (someone or something) "ignore" is from early 14c.
To know (something) like the back of one's hand, implying familiarity, is first attested 1893 in a dismissive speech made to a character in Robert Louis Stevenson's "Catriona":
If I durst speak to herself, you may be certain I would never dream of trusting it to you; because I know you like the back of my hand, and all your blustering talk is that much wind to me.
The story, a sequel to "Kidnapped," has a Scottish setting and context, and the back of my hand to you was noted in the late 19th century as a Scottish expression meaning "I will have nothing to do with you" [see Longmuir's edition of Jamieson's Scottish dictionary]. In English generally, the back of (one's) hand has been used to imply contempt and rejection at least since 1300. Perhaps the connection of a menacing dismissal is what made Stevenson choose that particular anatomical reference.