Interesting fact: A shadow is not a thing added to a scene. It is a region where light is missing or reduced because an object blocks it.
The answer: A shadow has no weight of its own because it is simply the absence of light, not matter. If you talk about the missing light energy, that energy has an equivalent mass, but the shadow itself does not weigh anything.
Shadows are conceptually tricky because they look like objects even though they are really patterns in illumination. Historically, they have been useful for measuring time, geometry, and the motion of the Sun, but not because they carry mass. Knowing that a shadow has no weight helps separate visual perception from physical substance.
