There is a very tiny washer underneath the lead weight that has the thread tied to it. That thread goes thru the lead weight, then thru the eyelet and then over to the tone arm pivot (to the outside). There is also a guitar string (high E) that runs from the plinth up thru the lead weight and into the eyelet. This "E-string" keeps the lead weight from swinging back and forth. The thread is about 2 lb test fishing line and has almost zero resistance thru the eyelet. As you swing the arm back and forth, the weight moves up and down. It really works great.
Oh, I get the mechanics of it, I have had several that were of the same general design. But they also had pulleys at the point where yours is sliding. I have retrofitted other people's with teflon dental floss to reduce the stick/slip motion when it slides. In some cases, you could see it stick and slip. We also used a rolling-contact on the tonearm side so the moment arm (and thus the torque) stayed the same throughout the travel. Without that, the effect is minimized if the thread is 90 degrees from the tonearm axis at the center of travel. Or you can make it a cam if you want to have the anti-skate vary predictably over the travel of the arm.
If you are interested, and you send me the dimensions (mostly, the height) I would be glad to take a stab at building a pulley and stand system. The rolling contact part, you are on your own. Not on any schedule, however - I got a lot of airplane stuff to work on in the next few months.
Brett