Let us consider a completely sealed weighing scale such that the air pressure above and below the pan of the scale are equal and is equal to 1 atm. pressure. The scale initially reads zero. Now if this weighing scale is placed in a completely evacuated chamber, will there be any change in the reading? I am guessing that as the force due to atmospheric pressure above the pan of the scale is now absent, but the air pressure below the pan is still present, the scale will show a negative reading as it experiences a net upward force which is equal in magnitude to the force exerted by the atmosphere on the pan initially. Is this reasoning correct? If not, what is the actual answer?
You must consider the effect of air pressure on each side of the pan when reading the weight, because the scale measures the exerted force, and this force can be exerted from the air pressure as well as any other object on the scale.
So, if the pressure below the pan is 1atm more than the pressure above, your explanation is correct and there will be a negative number.
Moving the scales from air to vacuum you would expect the reading to move in the same direction as if you had moved it from water (with 1 atm of air pushing down on the water) to air. The specific direction in either case would depend on whether the weighing mechanism relied on a sealed, compressible cavity.
A weighing mechanism based on the length displacement of suspending spring would give decreasing readings as the density of the fluid increased, due to buoyancy on the pan.
A weighing mechanism based on the volume displacement of a sealed cavity (piston compressing air chamber, calculating the force via gas laws) would give increasing readings as the pressure of the fluid increased. The pressure is important here depending on how vacuum is defined, as you can introduce heat energy to a partial vacuum and increase its pressure, even though there is no more gas and no less volume than there was before.