Final answer:
The box will remain stationary on the smooth table with the weights attached, as there is no external horizontal force acting on it to cause movement.
Step-by-step explanation:
In the scenario described, the box will not move upwards, downwards, towards the left, or towards the right due to the weights on the strings. Since the box is on a smooth table, and assuming there is no friction, the weights will not influence the horizontal movement of the box. The weight of the strings pulling on the box only applies a downward force due to gravity, which is counteracted by the normal force from the table. So, despite the weights, the box will remain stationary unless an external horizontal force is applied.