This word, meaning to leave a place, is commoner in America, than in England. In the sense of leaving off doing anything, it seems to belong to the U.S. (O quit! Quit that!)
1863. If there is to be no conciliation, we might as well quit the bill at once.—Mr. John B. Henderson of Mo., U.S. Senate, Jan. 30: Cong. Globe, p. 613/2.
1870. The elders at Nauvoo quit preaching about religion.—J. H. Beadle, ‘Life in Utah,’ p. 127 (Phila., &c.).
1882. The dog-catchers have quit going their rounds.—‘Texas Siftings,’ p. 62. (N.E.D.)
