What is this tool? I'm quite baffled.

[Bryan Burns]

This was part of a lot of tools I bought from fellow collector.
Had it for years and finally decided to cut the stitching on the sheath to uncover what I was thinking was some type of edge. Nope, it's not an edge tool.
Appears to be made of solid brass.

 

[wrenchguy]

Maybe copper? Maybe a soldering iron?

 

[Bryan Burns]

Maybe copper? Maybe a soldering iron?

May be copper but I don't see it being a soldering iron. I'm thinking some kind of leather working tool.

 

[Farmer J.]

Looks like it's the frame for one of those things we hand around in church for offerings. An 'Offertory'.
A bag dangles from the opening, and one hands it from person to person. Usually they have a round or oval opening between the handles.
Like this:

 

[4xdog]

Looks like it's the frame for one of those things we hand around in church for offerings. An 'Offertory'..:

Holy cow(!) In a thousand years I'd have never gotten that. I'll bet you're right. Well done.

 

[MR.X]

Is the inward curve different on either side? Why would an offering bag frame be curved in at all? The side closest seems to be smooth or finished....looks like it's been used to, for lack of a better word "bone" something, kind of like the way bones were used (ostensibly) to "compress" the wood on old Ash baseball bats.

 

[The Cobbler]

GJ never ceases to amaze me .

 

[txvwnut]

Looks like it's the frame for one of those things we hand around in church for offerings. An 'Offertory'.
A bag dangles from the opening, and one hands it from person to person. Usually they have a round or oval opening between the handles.
Like this:

I think we have a winner. We never had anything that fancy at the Methodist church, just a bowl to pass around and put a little pressure on those down the pew.

 

[Farmer J.]

Is the inward curve different on either side? Why would an offering bag frame be curved in at all? The side closest seems to be smooth or finished....looks like it's been used to, for lack of a better word "bone" something, kind of like the way bones were used (ostensibly) to "compress" the wood on old Ash baseball bats.

Yes, it does look as though it has been used like that, as though one side has been slightly bent in and rubbed on something. It also had that leather cover on the other side of it. Maybe it had been re purposed from an old offertory frame of maybe it's something completely different that just looks like one of them, I dunno

 

[ambenz]

I was going to say a specialized leather draw tool for finishing leather....

 

[RTM]

Looks like it's the frame for one of those things we hand around in church for offerings. An 'Offertory'.
A bag dangles from the opening, and one hands it from person to person. Usually they have a round or oval opening between the handles.
Like this:

Even the stitching piece the OP took off seems to match. Wow, nice work. I’d seen those bags visiting other churches, but never up close enough to look.