The photon box is a thought experiment involving a massless, perfectly reflective box containing light.
When the box is accelerated in any direction it results in a difference of force being applied to the walls of the box that are in line with the acceleration. The "front" being pushed less and the "back" being pushed more. This results in a resistance to acceleration or inertial mass and this mass can even be given a value in Kilograms regardless of the fact that no individual components are massive.
While I understand that this box is "massive" I do not know whether the box would have "weight".
Would the box fall in a gravity field?
If so, why?