A couple of thoughts:
3. The important aspects of a weight or clamp are (1) reduction in record warp; and (2) better contact between the record and the mat. Lesser effects include (3) greater inertial mass of the whole platter assembly (which adds rotational stability), plus (4) dissipation of vibration from the top surface of the record, into/through the weight/clamp (and possibly into the spindle. Obviously, if the platter is of the suspended type, the extra weight of the device will also alter the tuning of the suspension.
4. Whether and how much a clamp or weight affects the sound, will depend on all of the above interactions, and will vary from TT to TT.
I totally agree with this explanation and it is even more evidente when i use my Kenwood Stabilizing Ring