The strongest possibilities are antique mechanical or household weights, with old curtain/drapery weights and clock weights being particularly plausible based on their appearance. Antique examples of both categories can have loops, heavy metal construction, and decorative ribbed or textured surfaces.
Still, the exact identification should be treated as a mystery until the pieces can be compared with their original hardware or examined for markings.
So if you ever find something similar while cleaning an old family home, don't immediately put it in the trash—or on the Christmas tree.
Pick it up.
Feel the weight.
Look for markings.
And ask yourself a simple question:
What machine in this old house needed something this heavy hanging from a loop?
That question might be the key to uncovering a small piece of the home's forgotten history.