An actuation assembly for a cover extendable over an open-topped container body from a stowed position to a deployed position includes two actuator mechanisms on each side of the body, each including at least one torsion spring having a base portion and at least one reaction end and at least one reaction post in contact with a corresponding reaction end of the at least one spring. In a first exterior actuator mechanism, the reaction post is connectable to the bail arm, while in the second interior actuator mechanism the reaction post is mountable to the container body. A common shaft extends between the base portions of the spring(s) of each actuator mechanism to transmit torque from the interior spring(s) to the exterior spring(s), serving as a rotating anchor for the exterior actuator mechanism. Only the exterior actuator mechanism is situated outside the side extent of the container body.