Then again, a better question might be "how much less does an area covered in shadow weigh relative to surrounding areas covered in light?"
As Vsauce's Michael Stevens explains in the video up top, light has energy. This energy allows it to behave as though it has mass, and enables it to push any object on which it falls ever so slightly. This behavior is the same thing that makes it possible to alter the orbit of the Earth with little more than a bulb, a stand, a shade and an extension cord. It's also the physical property that makes solar sails possible.
Cool, right? That's just the beginning. Set aside a few minutes and let Stevens explain some of the oddities surrounding the speed of light, the "speed of push" and photonic booms. You'll be glad you did.