Old English stician "to pierce, stab, transfix, goad," also "to remain embedded, stay fixed, be fastened," from Proto-Germanic *stik- "pierce, prick, be sharp" (source also of Old Saxon stekan, Old Frisian steka, Dutch stecken, Old High German stehhan, German stechen "to stab, prick"), from PIE *steig- "to stick; pointed" (source also of Latin instigare "to goad," instinguere "to incite, impel;" Greek stizein "to prick, puncture," stigma "mark made by a pointed instrument;" Old Persian tigra- "sharp, pointed;" Avestan tighri- "arrow;" Lithuanian stingu, stigti "to remain in place;" Russian stegati "to quilt").
Figurative sense of "to remain permanently in mind" is attested from c. 1300. Transitive sense of "to fasten (something) in place" is attested from late 13c. Stick out "project" is recorded from 1560s. Slang stick around "remain" is from 1912; stick it as a rude item of advice is first recorded 1922. Related: Stuck; sticking. Sticking point, beyond which one refuses to go, is from 1956; sticking-place, where any thing put will stay is from 1570s. Modern use generally is an echo of Shakespeare.