It'll be heavier in vacuum (or even cold and/ or dry air, as compared with hot and/ or humid air...
The Montgolfier Bros was right about this already in 1782.)
Air pressure is higher on the lower side of the item than on its upper,
so the item sort of "floats insufficiently", relative to the massive Earth's gravity working on it.
Air has (like for instance, water) a buoyant force, as the item actually is "submerged" in air,
consisting of the weight of the air displaced by the item.
Oops- I forgot your question:
Replace the scale suspended container with a biggie cage of thin wires - chicken net.
-How big a force would the bird suspending pressure exert on the tiny wire area, do you think?