I literally weigh the air using a known volume, scale, and vacuum chamber.
Air has mass and therefor weight. This causes a buoyancy on everything in the air. That’s why weather balloons work. By removing air from a vacuum chamber, I reduce the amount of air and thus the buoyancy. The result is I weigh the volume of the air that was displaced by a cylinder that I 3D printed for the experiment.
As with all real life experiments, not everything goes perfectly to plan. I was expecting, at best, to achieve about 0.12g on the scale with the trials. There was rather more variation than I expected. I don’t have a good reason why. Essentially all I prove here is that air does have mass, just like water.
A basic theme in my FE videos is that F=MA and that gravity really does exist. You can’t measure something that doesn’t exist.
FE’s ask how can the oceans stick to a spinning ball. They should ask the same of the atmosphere. It is a giant ocean of air completely covering the earth. More to the point, what holds anything down at all? Gravity.
For sake of conversion between the barometer and the vacuum gauge, 10mb = 1kPa.