Why is it easier to slide a cardboard box when it is empty compared to when it is full of heavy books?

The amount of horizontal force needed to keep a box sliding along a horizontal floor is equal to the product of the coefficient of kinetic friction between the box and the floor and the normal force pushing up on the box from the floor, which is equal to the weight of the box. As long as the characteristics of the box and the floor remain the same (neither is polished, lubricated, etc.), the coefficient of kinetic friction remains constant. Therefore, the horizontal force needed to keep the box moving across the floor is directly proportional to the weight of the box.