Benefits of a record ring

FWIW, I use the TTweights ring, clamp and platter on my Raven One and like the results.

Bought myself a TTweights ring on impulse at the RMAF, using it on my Clearaudio Master Solution; it's only the 600 gram model, but all the improvements Redglobe hears on his system I hear on mine, and it's a third the price of Clearaudio's own ring (and being copper likely more effective). Amazing how much vinyl I've been spinning lately, a voyage of rediscovery.

I'm using the TT Weights ring and like it alot. My only concern is by using both the clamp and ring could impact negatively on the motor assembly not to mention belts, idler wheels etc. Does anyone have any comments on my caution?

It depends on the motor, belt, idler wheels, etc. If the table's design allows, helping the platter get going with a manual push removes most of the additional stress from those components. Once the platter's at speed a ring won't hurt them. If anything, the greater inertia will actually reduce demands on the drive train.

Another possible area of concern is whether your TT bearing can support the additional weight without wearing prematurely. Again, it depends on the table.

When I used a ring the most important benefit for me was the improved sinking of resonances out of the vinyl and into the platter, as others described. Flattening of warps was nice but most of my LP's aren't that warped. But they all benefit from a lower sound floor.

Can't use it any longer due to my tonearm, but I'd buy another if I could find one that fit.

I think an outer ring pressing down the record more firmly with a larger portion of its surface to the platter has a lot of benefit.
The possible drawback of too much additional load on the bearing - well, if a TT's bearing can't take the additional 2-5 lbs, it is hardly of any quality.
Furthermore the inertia of the platter is increased and the platter is kind of dampened. All these side-effects should and will - in a carefully set-up thread or belt driven TT - increase the overall performance. It is however important to add a good record clamp to the periphery ring.
On DD or idler drive TT's the increased inertia is counter-productive and it certainly needs some careful tests before going for this option.
Same is true for some 9" tonearms with conical armwands (SME V) - it often interferes with the increased diameter of the platter surface.
If your table and arm allows , I would always go for a periphery ring w/clamp.