"oily fat of land animals," c. 1300, from Anglo-French grece, Old French gresse, craisse "grease, fat" (Modern French graisse), from Vulgar Latin *crassia "(melted) animal fat, grease," from Latin crassus "thick, solid, fat" (source also of Spanish grasa, Italian grassa), which is of unknown origin. Grease paint, used by actors, attested from 1880. Grease monkey "mechanic" is from 1918.
adjective suffix, "full of or characterized by," from Old English -ig, from Proto-Germanic *-iga- (source also of Dutch, Danish, German -ig, Gothic -egs), from PIE -(i)ko-, adjectival suffix, cognate with elements in Greek -ikos, Latin -icus (see -ic). Originally added to nouns in Old English; used from 13c. with verbs, and by 15c. even with other adjectives (for example crispy).
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Harper, D. (n.d.). Etymology of greasy. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/greasy