wiktionary
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From snot + -y.
etymonline
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snotty (adj.)
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.
