How would I go about measuring the weight of my shadow? Wait!! Now here me out....?

It's a clever question but technically you are measuring the difference in force on the surface of the earth between when it is exposed to sunlight and when it is largely blocked. Let's assume for the moment, that you completely block the light coming to a patch of ground (scattering from the atmosphere and surrounding objects makes this impossible, but play along) and that patch has an area A. We know both classically and quantum mechanically that light exerts a force due to momentum transfer when it encounters a surface. There are two momentum transfer mechanisms - absorption and reflection - and an arbitrary surface can do both at the same time. The pressure due to sunlight at the surface of the earth (neglecting atmospheric absorption) is

Absorption Pa = 4.54 cos(q) uN/m^2 where q = zenith angle of sun

Reflection Pa = 9.08 cos(q) uN/m^2

If you had a surface that could be perfectly reflecting and perfectly absorbing (not possible) then you could sum the two pressures but in essence, you are looking at ~ 10 uN/m^2.

To measure this difference, you'd need a very sensitive strain gauge attached to the surface you were doing the experiment on Ideally, you'd set up a surface supported by a weak spring (or sets of springs) and measure the stress (alternately measure the surface displacement but they'd have to be really weak springs) then completely put the surface in shadow repeat the measurement. Good luck

The "weight" of the shadow would be so small, it would not be practical to measure it. The slightest breath of air would be hundreds of times more than the weight of the shadow. Our technology is just not yet capable of measuring such small differences in weight.

Unless ... you were in outer space, far outside the atmosphere. Then perhaps you could measure the difference in light pressure on a "solar sail", with and without your shadow on it. This has been calculated as 9.08 microPascals (at the Earth-Sun) distance, which translates to about 10 million times less than Earth gravity.

the main issue is one of scale and resolution. you would not try to measure the size of a cell using a meter stick, as an analogy. the weight of a shadow is very small under earth surface conditions and most weighing equipment is incapable of detecting the differences involved. Even if you could find a technological system that could measure the fine differences involved, you would then face the issue of signal to noise ratio. There are forces involved in addition to those resulting from light and gravity, such as fluctuations in air pressure, and these variations would dominate the signal at the scale (resolution) required to detect the differences in force on the object resulting from removal of light. You would require isolating the object of measurement from most if not all forces other than those of gravity (and perhaps even gravity) and light in order to actually be able to see the change. the change you seek is so tiny that it will not be identifiable under most circumstances.

According to various sources on the internet (who might have copied off each other) the force of sunlight in space at the distance of the Earth from the Sun is 9 Newtons per square kilometre.