cheese (n.1) Look up cheese at Dictionary.com
Old English cyse (West Saxon), cese (Anglian) "cheese," from West Germanic *kasjus (cognates: 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" (cognates: 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"). 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 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 was a schoolgirls' amusement (1835) 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 curtsey."
cheese (n.2) Look up cheese at Dictionary.com
"the proper thing," from Urdu chiz "a thing," from Persian chiz, from Old Persian *ciš-ciy "something," from PIE pronomial stem *kwo- (see who). 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 (v.) Look up cheese at Dictionary.com
"stop (what one is doing), run off," 1812, thieves' slang, of uncertain origin. Meaning "to smile" is from 1930 (see cheese (n.1)). For meaning "to annoy," see cheesed.
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]