c. 1400, "keep from view or use, render inaccessible" early 15c., "to lock up, confine," from shut (v.) + up (adv.). The meaning "cause to stop talking" is from 1814 (Jane Austen). The intransitive meaning "cease from speaking" is from 1840, also as a command to be silent, sometimes colloquialized in print as shuddup (1940). Put up or shut up "defend yourself or be silent" is U.S. slang, by 1868.
1830 as the name of a children's game (OED describes it as "all-fours" when played for seven "chalks"); with capital initials, as the proprietary name of a brand of carbonated drink, it is attested from 1928.
"adjustments made to an automobile to improve its working," 1911, from verbal phrase tune up "bring to a state of effectiveness," 1718, in reference to musical instruments, from tune (v.) + up (adv.). Attested from 1901 in reference to engines. Meaning "event that serves as practice for a later one" is from 1934, U.S. sports jargon.