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.
1560s, "directed downward," from down (adv.). Sense of "depressed mentally" is attested from c. 1600. Slang sense of "aware, wide awake" is attested from 1812. Computer crash sense is from 1965. Down-and-out "completely without resources" is from 1889, American English, from situation of a beaten prizefighter.
1710, "a downward movement," from down (adv.). Football sense of "an attempt to advance the ball" is by 1882.
"in a descending direction, from a higher to a lower place, degree, or condition," late Old English shortened form of Old English ofdune "downwards," originally of dune "off from (the) hill," from dune "from the hill," dative of dun "hill" (see down (n.2)). The "hill" word is general in Germanic, but this sense development is peculiar to English. As a preposition, "in a descending direction upon or along," from late 14c.
To be down on "express disapproval of" is by 1851. Down home is from 1828 as "in one's home region," as an adjective phrase meaning "unpretentious" by 1931, American English. Down the hatch as a toast is from 1931. Down to the wire is 1901, from horse-racing.
Down Under "Australia and New Zealand" attested from 1886; Down East "Maine" is from 1825; Down South "in the Southern states of the U.S." is attested by 1834. Down the road "in the future" is by 1964, U.S. colloquial. Down-to-earth "everyday, ordinary, realistic" is by 1932.
1560s, "cause to go down," from down (adv.). Meaning "swallow hastily" is by 1860; football sense of "bring down (an opposing player) by tackling" is attested by 1887. Figurative sense of "defeat, get the better of" is by 1898. Related: Downed; downing.
"first feathers of a baby bird; soft covering of fowls under the feathers, the under-plumage of birds," used for stuffing pillows and feather-beds, mid-14c., from Old Norse dunn, which is of uncertain origin. Extended in Modern English to the soft hair of the human face and fine soft pubescence upon plants and some fruit.
"a hill of moderate elevation and more or less rounded outline," Old English dun "height, hill, moor," from Proto-Germanic *dunaz- (source also of Middle Dutch dunen "sandy hill," Dutch duin), "probably a pre-insular loan-word from Celtic" [Cambridge Dictionary of English Place-Names], in other words, borrowed at a very early period, before the Anglo-Saxon migration, perhaps from PIE root *dheue- "to close, finish, come full circle."
The more general meaning "elevated rolling grassland; high, rolling region not covered by forest" is from c. 1400. Specifically of certain natural pastureland districts of south and southeast England (the Downs) by mid-15c.
The non-English Germanic words tend to mean "dune, sand bank" (see dune), while the Celtic cognates tend to mean "hill, citadel" (compare Old Irish dun "hill, hill fort;" Welsh din "fortress, hill fort;" and second element in place names London, Verdun, etc.). German Düne, French dune, Italian, Spanish duna are said to be loan-words from Dutch.