Feltwad, Neat rifle, and to me it looks like one typical made in the 1840s / 1860s.
The extra big barrel and the buckhorn sight certainly give it that Plains Rifle look, and it probably is a Western made ( West of the Mississippi) rifle, so certainly would be considered as a Plains Rifle. By that time period there was little use for a 50 cal back east, but still plenty of big game out west. The Buckhorn was also an out west type of sight.
No cheek piece is a bit unusual, but not unheard of. Is there any signs of a cheek piece having been there originally? Also, I wonder if there's any indication that the barrel has been shortened from the breech end, as 31 inches seems a bit short.
Dave B mentioned the possibility of a target rifle, and that possible, but I'd think probably not. I think it's just a big barreled gun made for heavy loads. Today's rifles tend to be on the lighter side, but several of my old Kentucky's weigh in at 10 to 12 pounds so I don't think that weight was as much an issue as today. Consider that most western guys were used to manual labor and weren't fat and out of shape couch potato's like a lot of people today, so lugging what we think of as a heavy rifle wasn't that big of deal.
I doubt you'll find any markings inside the lock, but there might be a barrel makers name stamped on one of the under side flats of the barrel back near the breech. An inside picture of the lock works would be interesting, and show what quality the rifle was originally built too.
All in all it looks like a pretty nice rifle, and any addition pictures would be appreciated! And I'll be it went pretty inexpensively over your way!
John