early 14c., "quilted material worn under chain mail," from Old French estoffe "quilted material, furniture, provisions" (Modern French étoffe), from estoffer "to equip or stock," which according to French sources is from Old High German stopfon "to plug, stuff," or from a related Frankish word (see stop (v.)), but OED has "strong objections" to this.
Sense extended to material for working with in various trades (c. 1400), then "matter of an unspecified kind" (1570s). Meaning "narcotic, dope, drug" is attested from 1929. To know (one's) stuff "have a grasp on a subject" is recorded from 1927.
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 stuffy. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/stuffy