The maximum weight a suction cup can hold depends on the force created by the atmospheric pressure pushing it against the ceiling. This force (F) is calculated by the formula: $F=P\times A$, where P is the external air pressure and A is the area of contact. Since the internal pressure is nearly zero, the entire external pressure acts on the area. Therefore, both the outside air pressure and the contact area determine the maximum supported weight.

Final Answer: both its area of contact with the ceiling and the air pressure outside the cup