"proud, arrogant," 1918, noted that year as college slang, from snoot (n.) + -y (2). Probably with suggestions of snouty (1858); the notion being of "looking down one's nose." Related: Snootily; snootiness.
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).
<a href="https://www.etymonline.com/word/snooty">Etymology of snooty by etymonline</a>
Harper, D. (n.d.). Etymology of snooty. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/snooty