1530s, in reference to water-wheels, "driven by water shot over from above," past-participle adjective from overshoot. In old slang also "having exceeded the proper limits in drinking, drunk" (c. 1600).
Entries linking to overshot
overshoot v.
mid-14c., "to shoot, run, or pass beyond (a point or limit), exceed, overstep," over- + shoot (v.). Meaning "to shoot over or beyond" (a mark or target) is by 1540s. Related: Overshot; overshooting.