You could, in a lathe, It's sketchy. You could bolt it up to a shaft through the center. Its still a big interrupted cut and you'd risk destroying it, from your posted image. I cheapest: a bucket of water and a $60 hf belt sander. Install an axle and do your due diligence and take your time keeping it round and your fingers cool!
There's not a lot of material between the 4 holes on the solid side and the outer edge, so you would only get minimal cleanup. If you could use the inside threadded holes you'll be able to remove more material. Unless you have access to a machine shop, this may be a difficult task by yourself. Can you post a pic without the jnuckle installed, flat side down? Brass/bronze is hard to machine, as it's "gummy" .
I've used my wood lathe to turn down weights before. However they were much easier to chuck up and center. I've used the wood turning carbide tools on one project and I've used just sandpaper on another.
Just to clarify are you wanting to take material off the faces or the outer diameter?
I assume you've already got the wheels picked out. If not what about a high offset wheel like TGH's: TGH-HH H.O. V1.1 BRASS WHEEL BODY
Or are you able to modify the inside of the wheel to gain a little clearance? Maybe a little clearance from the wheel could mean removing less material on the weights? Pics of the wheel would be helpful too.