1In or into a position with the belly or underside facing upwards; specifically (especially of a fish) in or into this position as the result of dying.
2US figurative, informal In or into a situation of having failed (especially financially), died, finished, or become defunct. Especially in "to go belly-up".
Mid 18th century; earliest use found in William Douglass (?1691–1752). From belly + up.