Based on your experiments, my guess is there is a problem with the arm, or arm setup.
You should perhaps look into using Hi-Fi News Analogue Test LP for setting up the anti-skating. There are four tracks used to the setup the anti-skating. You should get it to track the first three of the anti-skating tracks and the tonearm should be fine, as far as anti-skating goes.
If possible, for setting the vertical tracking force, make sure that the tonearm rests parallel to the platter while the tip of the stylus is on the scale. The weight reading will change depending on whether the arm is parallel or not, with the stylus resting on the scale. Based on the scales available today, the tonearm should probable be raised a bit for setting the VTF, and then move down the VTA again to play.
Best,
iSanchez