These are several unusual balance weights for slide-tuning trombones made by James New at Kanstul. They clamp around the tapered neckpipe adding some needed balance to a slide-heavy horn. The hole doesn't go through the center of this balance weight like most others. Instead it's drilled off to the side so when clamped around the neckpipe, most of the weight is on the inboard side of the trombone body.
Two of the weights fit Kanstul 1606ST, and may be about the right size for an older small-bore Conn trombone with tuning in slide. I can't say exactly. I think Jim said he tapered the channels to follow the expansion of the neckpipe. Cool.
The larger bore weight fits Kanstul 1608, or with included shims, Kanstul 1662/1662I. The label says .710", which is the 1608 (.547" model) neckpipe size.
Other dimensions and fit are unknown. In slightly gold tinted lacquer, with screw and two stickers.