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past tense of hang; meaning "having impressive male genitals" is from 1640s; of a jury, "unable to agree," 1838, American English. Hung-over (also hungover) in the drinking sense is from 1950 (see hangover); hung-up "obsessed" is from 1961.
Obsessed with; stalled or frustrated by; suffering a hangup over: I'm hung up on fried rice (1957+ Beat & cool talk)