I have used a variety of copper mats in conjunction with weights & washer or reflex clamp & washer on a variety of TT's and in my experience hard mats such as stainless or copper always sound better with a proper clamp system designed to couple the record to the mat. Without a clamping system the results lack focus.
Listening to a variety ( copper, stainless, original & resomat ) on the mongrel version of the Krebs Technics SP10 in the same system showed me that none of the mats were perfect. Based on my own experience I believe this was due to the lack of a clamp with the metal mats.
Same result with the Goldmund Mat, which I have heard on the Goldmund, Sota, Oracle & Technics SP10, it sounds much better used in conjunction with the reflex clamp.
Most weights manufactured today do nothing unless the record mat/platter is slightly concave because they have a flat bottom and cannot apply pressure at the perimeter of the record label to clamp over a washer placed under the record.
Very few records are truly flat, and therefore unless you are using a soft mat such as felt or leather then the records are not supported across their entire surface on a hard mat such as metal or acrylic unless a clamp/weight is used and has been designed properly, that is either the record mat is slightly concave as in the goldmund, or a washer/reflex clamp system is used.
I am not sure why anyone would put a clamping ring under the record, unless of course they are superman and wear their undies over the top of their trousers.