Back to the magnets. The plate should swing approximately halfway between them. On my scale there is a fairly large gap on each side of the plate, maybe 1/8".
In the interest of science (called my curiosity), I just disassembled my scale to see if the orientation of the magnets makes any difference. It makes a big difference! When I put it back together with the magnets not oriented N-S, the beam oscillation went on and on, i.e, there was no damping. I stopped after about 10 oscillations. When I put the magnets back in their original N-S orientation, the beam stopped dead still after 2 oscillations.
To check the magnets, you'll have to remove them. In my scale (an Ohaus as are most scales no matter whose name is actually on the outside), there is a screw and a U shaped non-ferrous retainer holding the magnets in place. If you can get the magnets out, let them touch each other. If they are correctly oriented, they will stick to each other squarely (mark the top of each of them at this point). If not, they will still stick to each other, but not until they are clearly off center. Replace the magnets with the marks in the same position as when they were being tested.
Did you buy the scale new or used? If used, someone may have messed with the magnets. Actually, even if new, they could have been installed incorrectly.
If the magnet test doesn't prove anything, then, like several others, I suspect a wind draft. I also tested that with a very gentle breeze and it definitely affected the operation of the scale - the beam would oscillate far too long.