I searched a few hours through the Kamon crest 5000+
Kanji - Chinese, Japanese, etc.
No where did anyone ever use a "Circle with a S"
I thought maybe the stone was the "Circle" and
the metal was the Crest design, it does not show
in any Kamon crest.
Okinawans used a "Surujin" same design as the
"Kusari-fundo" and were more common to use rocks
as weights using rope and chain.
Japanese culture had so many weapons bans the
Surujin and the kusari-fundo type weapons became
common as they were easy to conceal.
Might be that the stone and metal are not even
from that region, and brought by travelers.
I even searched Indonesian, Indochinese, etc.
never found a mark that correlates with what you have.
It was fun research to say the least.
Good Luck
Shaolin monks don't even use those marks and
and they showed up quite early in Okinawa.