late 14c., "a cot, a humble habitation," as of a farm-laborer, from Old French cote "hut, cottage" + Anglo-French suffix -age (according to OED the whole probably denotes "the entire property attached to a cote"). Old French cot is probably from Old Norse kot "hut," cognate of Old English cot, cote "cottage, hut," from Proto-Germanic *kutan (source also of Middle Dutch cot, Dutch kot).
Meaning "small country residence or detached suburban house" (without suggestion of poverty or tenancy) is from 1765. Modern French cottage is a 19c. reborrowing from English. Cottage industry, one that can be done at home, is attested from 1854. Cottage cheese, the U.S. name for a kind of soft, white cheese, is attested from 1831, earliest in reference to Philadelphia:
There was a plate of rye-bread, and a plate of wheat, and a basket of crackers; another plate with half a dozen paltry cakes that looked as if they had been bought under the old Court House; some morsels of dried beef on two little tea-cup plates: and a small glass dish of that preparation of curds, which in vulgar language is called smear-case, but whose nom de guerre is cottage-cheese, at least that was the appellation given it by our hostess. ["Miss Leslie," "Country Lodgings," Godey's Lady's Book, July 1831]
curd of milk coagulated, separated from the whey, pressed and used as food, Old English cyse (West Saxon), cese (Anglian) "cheese," from West Germanic *kasjus (source also of Old Saxon kasi, Old High German chasi, German Käse, Middle Dutch case, Dutch kaas), from Latin caseus "cheese" (source of Italian cacio, Spanish queso, Irish caise, Welsh caws).
Of unknown origin; perhaps from a PIE root *kwat- "to ferment, become sour" (source also of Prakrit chasi "buttermilk;" Old Church Slavonic kvasu "leaven; fermented drink," kyselu "sour," -kyseti "to turn sour;" Czech kysati "to turn sour, rot;" Sanskrit kvathati "boils, seethes;" Gothic hwaþjan "foam").
But de Vaan writes, "no etymology can be found which does not require some poorly-founded assumptions," and suggests a loan-word. Also compare fromage. Old Norse ostr, Danish ost, Swedish ost are related to Latin ius "broth, sauce, juice."
Earliest references would be to compressed curds of milk used as food; pressed or molded cheeses with rinds are from 14c. Transferred to other cheese-like substances by 1530s. As a photographer's word to make subjects hold a smile, it is attested from 1930, but in a reminiscence of schoolboy days, which suggests an earlier use. Probably for the forced smile involved in making the -ee- sound.
Green cheese is that newly made; the notion that the moon is made of green cheese as a type of a ridiculous assertion is from 1520s. To make cheeses (1835) was a schoolgirls' amusement of wheeling rapidly so one's petticoats blew out in a circle then dropping down so they came to rest inflated and resembling a wheel of cheese; hence, used figuratively for "a deep curtsy." Bartlett ("Dictionary of Americanisms," 1848) defines head cheese as "The ears and feet of swine cut up fine, and, after being boiled, pressed into the form of a cheese."
"the proper thing" (slang), from Urdu chiz "a thing," from Persian chiz, from Old Persian *ciš-ciy "something," from PIE pronominal root *kwo-. Picked up by British in India by 1818 and used in the sense of "a big thing" (especially in the phrase the real chiz).
This perhaps is behind the expression big cheese "important person" (1914), but that is American English in origin and likely rather belongs to cheese (n.1). To cut a big cheese as a figurative expression for "look important" is recorded from 1915, and overlarge wheels of cheese, especially from Wisconsin, were commonly displayed 19c. as publicity stunts by retailers, etc.
The cheese will be on exhibition at the National Dairy Show at Chicago next week. President Taft will visit the show the morning of Monday, October thirtieth, and after his address he will be invited to cut the big cheese, which will then be distributed in small lots to visitors at the show. [The Country Gentleman, Oct. 28, 1911]
CHEESE IT. Be silent, be quiet, don't do it. Cheese it, the coves are fly; be silent, the people understand our discourse. ["Dictionary of Buckish Slang, University Wit, and Pickpocket Eloquence," London, 1811]