Can shadows affect gravity? I was watching a video on Youtube (Vsauce, great channel, check them out), and they were talking about how much a shadow weighs, and he was talking about sails that were pushed by light. He said an area covered by shadow technically weighs less then a area not covered by shadow and being pushed by the light. 
Does that mean if I could perfectly control how much energy I put into jumping, and jumped once in the light and measured it, Then jumped once in the shadow and measured it, (using the same amount of force to get off the ground each time) I would go a almost noticeable distance higher in the shadow? Since gravity is slightly different in all places on Earth just assume the areas I jumped in had the same amount of gravity on each places I jumped. So would the shadowe affect it at all?
 A: The answer is yes but only up to a point.

If I jump in sunlight and under a sunshade, all other factors being equal, will I jump higher in the shade?

Yes, you will jump higher. This is due to the radiation pressure that pushes you down when you are exposed to downwards-pointing sunlight.
However, this effect is not at all likely to be measurable. Radiation pressure due to the Sun at the Earth is of the order of 10 µN/m2, which is an essentially negligible amount compared to the ~1 kN force with which gravity acts on you. A simple experiment like this will not be able to show the differences and they will be drowned in the noise from e.g. the uncertainty in your initial kick-off. (On the other hand, a carefully designed experiment, like a solar sail, can indeed show the effect.)

Thus far so good: the effect is real (albeit tiny). The problem, though, is that it is completely incorrect to say that shadows "affect" gravity. Gravity is, by definition, proportional to the object's mass. Radiation pressure, however, does not care at all about the mass, but rather about your albedo and cross-sectional area. They're two completely different things. There's nothing wrong, though, with having multiple forces acting on a body, in the same way that air resistance and buoyancy also make slight corrections to your gravitational trajectory when you jump.
