1560s, "full of snot," from snot + -y (2). Meaning "impudent, curt, conceited" is from 1870. Related: Snottily; snottiness. Snotnose "upstart" is from 1941; snotty-nose "contemptible fellow" is from c. 1600.
late 14c., from Old English gesnot "nasal mucus," from Proto-Germanic *snuttan (source also of Old Frisian snotta, Middle Low German and Middle Dutch snotte, Middle Low German snute), from the same base as snout. Old English also had a verb snite "wipe or pick one's nose." Meaning "despicable person" is from 1809.
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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Definitions of snotty from WordNet
(used colloquially) overly conceited or arrogant; "a snotty little scion of a degenerate family"-Laurent Le Sage;