The cart experiences a frictional force which is directly proportional to its weight. This means that there must be a force applied on the car to balance the forces on the car to produce a net force of 0.
This is in accordance to Newton's first law which states that an object at rest will remain at rest and an object in motion will remain in motion unless an external force acts on it. The force must be a resultant force.
Therefore, the force needed increases with the total weight of the cart as well as with the added mass in a linear manner.
