Why are my woofers pumping?

Your problem is most likely a combination of ununiform belt thickness, not precise pulleys, motor rumble, not precise bearing. They all combine and create a mechanical shimmer in the turntable's suspension. 

While playing the runout groove and watching the woofers move in and out. Gently, but firmly place your hands on the plinth and try to very carefully hold it in place. The woofers should move in and out less.

Still even though it still falls within the 8hz range, I believe the ideal range would be closer to 10hz.  so if you buy a cartridge that you think has a compliance of 12 and it is really closer to between 16 and eighteen, i would think that would be audible at some frequencies which could be bothersome for some people.  its kind of deceiving as I did not even notice the whole 100 hertz thing until after I bought my cartridge.  It still sounds good but it is not what I thought I was getting.  for instance when I bought a benz cartridge and its compliance was 16, it was 16.

tzh21y - yes I think the same. Maybe even small things help, getting the resonance up. Stripping the arm of all extra mass and changing the counterweight position, like Atmasphere suggested.
Invictus, Almarg - I don’t think the player is the problem, behaves much better than my former VPI. The plinth is dead stable as it is. Belts - maybe new ones would be better, but this is not the main cause.
Somehow, the pumping has decreased a bit over the last days. Not sure which of my modifications that made the change.
The pumping is now very evident when I turn the volume up to 92-96 db from the listener position - measured when playing music. Going down to 88-90, where I usually listen, it is not so notable. I must test this more, trying to find "silent" vinyl grooves.
Atmasphere - I was not aware that loading could influence the resonance - ? I load the Atlas at 475 Ohm, but could go down to 100, have not tried yet.

Why don't you try what I posted...

Invictus005: I've tried your suggestion now, holding the plinth, but it makes no difference. This is a very heavy player (83 lbs). I used the runout on the Hifi News test record. And noticed, once more, that the woofer pumping is much reduced, compared to some days ago. In fact, it now looks/feels more like normal vibrations. And this is with the volume very loud (95+ db when playing music). So, where did the pumping go? I have a prolapsis so testing takes a bit of time. I wish I could tell you more exact what has caused the reduction of the problem. Besides reducing the effective mass, I did take off the platter, checked the spindle and moved the steel ball a little.

I also discovered that, indeed, "silent" record grooves are not the same. I have a UK original of Pink Floyd: Meddle, that plays amazing, especially side B (Echoes), with "HTM" in the deadwax, which means Harry T Moss "cutter extraordinaire at EMI UK" from what I read. In the silent-to-quiet opening of Echoes, the woofers pump a lot (on high volume). Is it a problem? Rather, I get the impression, this was intended by Mr Moss, to get the absolute best from the recording. As the music gets louder, I don't see the pumping (since the musical energy now grabs the woofers), although it may be there, in the background. This is what I suspect, and the reason I wanted to improve the situation in the first place. I think that this relates to a more "tense" or "disturbed" sound, and also, to a bit of break-up of the woofers at high volume (in sum - creating more listening fatigue). Btw the woofers are Acoustic Elegance TD10X (four of them in my system).

Testing again, with the HiFi News record side B band 6: Unmodulated groove (check residual system noise). Not much pumping even at unrealistic high volume. Even this track is not fully silent (what record is?) and the cone movement is in line with what I hear, indicating - I think - that indeed, the cartridge/arm combo has become less over-eager down at 5-6 Hz. I tested the runout on some other high quality records also - MFSL, ECM - same result.