Before I went to filing I would do a thorough cleaning of the contact points on the beam scale. They are usually very fool proof (it's all I use and have for decades).

It's possible something is loose in the 1/10th adjuster. Some have a weight that runs up and down a threaded rod. Make sure that rod is secured.

Clean the "V" and arms on the beam that set in it.

Make sure it is absolutely level and on a solid surface. It didn't loose a foot or pad underneath?