I thought the rigid circle was only for field. Looking at
GNAS RoS there's nothing mentioning the circle until you get to the field section where it says something like "in addition to the above stuff for recurve barebow..."
Thanks Chris B but which weights do you mean? That links straight to the alt services front page. Under Stabilisation/Weights I find the cartel compound hunter being 5/16 and Leven industries but nothing that would add 140g to the bow.