A counterbalance assembly for an appliance has a guide member with a rotatable pulley with a fixed radius and a cam affixed to one side of the pulley and having a varying radius. The cam and the pulley rotate about a pulley axis of rotation as a single unit. The counterbalance has a force applicator that applies a counterbalance force to one of the pulley or cam, and the counterbalance has a connector that couples the other of the pulley or cam to the door. The counterbalance force applies a varying counterbalance torque to the door that is a function of the ratio between the fixed radius and the varying radius over the pivotal range of the door.