Taking a guess, at a big meaty ball gun that was bored out and re chambered for the next size up?
Could have been a heavy barreled 11 gauge or other obsolete case that was bored out which might explain why its quite thin at the breech, if it had been rifled or some kind of slug gun it would explain the presence of the evidence of sights, and just to really clutch at straws whoever bored it out might have scrubbed the marks when he did the work.. i really don't know.. interesting though.
Some early breach loaders ( some pinfires i have ) were quite thin at the breech, if it was not for the radius on the action i might have suggested a pinfire convert.
Has he shot it? what does it feel like and swing like?
Nice find though.