Two more thoughts:

Ohaus (who make the RCBS/Hornady/Lyman/Lee, etc. beam scales scales) are magnetically dampened. If you have anything nearby with a strong magnetic field you may be impacting it.

I have my beam scale setting on a pane of glass removed from an old picture frame. As flat a surface as can be found in most homes.

A good test is to zero the scale, then weigh a bullet (I use Sierra MatchKings - they run very true to labeled weight) and reset to zero and see if it repeats the zero index. Or you could spend the $ on a scale standard weight kit.