Old English cyse (West Saxon), cese (Anglian) "cheese," from West Germanic *kasjus (cf. 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" (cf. 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 cf. 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."