First question : are the scales you use modern electronic scales based on load cells, or are they the more or less antique stuff with weights on one scale and the object on the other.

In the fist case (with the load cells) your reading will increase with increased vaccuum. The upward force, due to Archimedes and his law, will decrease because the density of the surrounding fluid (i.e. air) decreases.

In the second case, it will depend on the density of the object compared to the density of the weights. Example : you have one kg of cork on the object scale, and a 1 kg copper weight on the other. Since the cork displaces more air than the copper (for the same weight), the upward force on the cork will be greater. If you see the scales in equilibrium, the actual MASS of the cork will be greater than the mass of copper. If you put the scale in vaccuum the scale will tip over to the cork side.

On the other hand, if you increase the air pressure (10fold for example) the scales will tip over to the side of the copper weights.