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1. Continue what one is doing, endure something to the end, as in I hate large parties but I promised her I'd stick it to the end. [Early 1900s] Also see stick out, def. 2.
2. Also, stick it or shove it up one's ass . Do whatever you like with it, I don't want it, as in Do that job all over again? Why don't you stick it?, or Tell the chef he can take this fish and shove it up his ass. This vulgar slangy idiom, which uses stick in the sense of "thrust inward or upward," also functions as a variant of up yours. [Second half of 1800s]
See also: stick