The story
* Sense of “hoist with a jack” is from 1885; then, “increase prices, etc.” (1904, American English); both ultimately from noun jack (“mechanical device used to raise heavy objects”) * “Screw up, mess up” sense derived from, or influenced by fuck up, as a bowdlerization; also possibly influenced by jacked up (“high, intoxicated”) * First dialectal idiomatic meaning: “abandon, give up” (1873), possibly a corruption of chuck up, as chuck up the sponge (“give up, concede, give token of submission”)
Etymology from Wiktionary, CC BY-SA 4.0.