"excessive or misleading publicity or advertising," 1967, American English (the verb is attested from 1937), probably in part a back-formation of hyperbole, but also from underworld slang verb hype "to swindle by overcharging or short-changing" (1926), itself a back-formation from hyper "short-change con man" (1914), from the prefix hyper- meaning "over, to excess."
Also possibly influenced by drug addicts' slang hype, shortening of hypodermic needle (1913). Related: Hyped; hyping. In early 18c., hyp "morbid depression of the spirits" was colloquial for hypochondria (usually as the hyp or the hyps).