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).
an overshot jaw
overset
oversexed
overshadow
overshoe
overshoot
overshot
oversight
oversimplification
oversimplify
oversized
oversleep