Thanks for asking our advice
Surprizing to find RCBS scales that are inaccurate. By the way, Ohaus makes the scales, as well as those sold bearing the paint and nameplate of Dillon and almost all others except Lee.
If the fulcrum (knife-edge and jewel) points are full of dust, gunk or are cracked, bent or worn you will get bad readings. Cleaning works for dust and gunk. Replacing the parts (that means sending the scale back) works for the rest.
You mentioned zeroing the scale, so I will assume you are doing everything else right But for one exception: While the scale is still settling, watch the pointer as it swings up and down. Is the movement a perfect, decaying sinusoid? Or does it "catch" and jerk and vary in speed? Does it swing up to a point, then down to a point then up again to a point not quite as high as the first time and then down to a point not quite as low as the first time and repeat this decaying amplitude until the pointer is still? (Similar to the decay you observe if you let a golf ball on a hard surface until is comes to rest)
Sometimes the fulcrum binds just from the beam not being centered in the jewel bearings. If either end of the knife-edge touches the end of the cradle your beam will never work right, so make sure it is centered. Likewise if the copper plate that provides magnetic damping rubs on anything.
Other than binding of the beam (at the fulcrum or other point), there is virtually nothing that can prevent repeated measurements from being precisely the same every time. Balance is balance.
If your sliding weights (on the 10-10, I include the threaded weight, too) are the right weight and the markings in the right positions, there is nothing that can prevent measurements from being correct (as long as you are close to the surface of the Earth and stationary). Gravity is gravity and doesn't change much.
1) The scale must be on a stable surface. Put it on a concrete slab floor if you have to.
2) Make sure there is NO air movement. That blows (pun intended) all reasons out of the water. If you have to, put a cardboard box over the whole thing and watch it through a small (1" maybe) hole and a flashlight.
3) Make sure your beam is not touching anything (binding) and is completely free in its movements and that those movements are up/down only, not any side to side or lengthways. (Gently wiggle the beam to settle it into its lowest position.)
4) Make sure your bearings and knife-edge are clean and in good condition
5) Test your beam by watching it oscillate and settle down. Then do it again to verify that the oscillations decay smoothly and that it settles in the same place.