Final answer:
The box is supported against gravity by the normal force, which acts perpendicular to the surface and counteracts the object's weight.
Step-by-step explanation:
The force responsible for supporting the box against the force of gravity is the normal force. The normal force is a contact force exerted by a surface against an object that is resting on it. This force acts perpendicular to and away from the surface. It is equal in magnitude and opposite in direction to the weight of the object, which is the force of gravity acting on it. The normal force arises because the surface is slightly deformed when the object is placed upon it, causing the surface to push back against the object, much like a compressed spring.