I can't speak for thr master, Harry Weisfield, and possible he might even chime in to concur with my thoughts, but I'm largely under the impression Harry designed the Heavy Centerweight to work in conjunction with the Periphery Weight Ring. Of course it can be used without, as is mentioned previously, minus Rubber Washer, but I'm of the impression that the Threaded Clamp, even the inexpensive version that came with the 19Jr is a better way to go.
One can more precisely monitor clamping force, using just enough, without strangling your LPs to death. With the Weight, there's no variance, nor adjustability. Sure, your Label Area might be coupled to Platter, but maybe little else? I would think a larger percentage of your LPs will not benefit from the Weight.
Now, moving onto your last post, and mention of surface noise. I'm of the impression that this is not at all related to any clamping method, but more than likely the Cartridge you are using? If it is noted on all of your LPs, it might be safe to say, that it is not a cleaning issue, but it could be?
Tell us some more facts about your system, as I'm sure others here will then know better what weak point is in your particular analog rig. Tell us what Cartridge, Phono Stage, etc. Might be time for a Cartridge upgrade? Mark