The early barrels say prior to 1812 were hand forged. During the forging of the laps around the mandril the barrel would be larger at the breech and muzzle and narrow thru the length of the barrel.
The later barrels were hammer mill forged mass produced by firms like E. Remington & Sons. These barrels had the straight walls like the modern barrels of today. This occured about the same time the Perc. cap was the favored form of ignition.
The rifle you have appears to be a straight wall and small caliber under .50 caliber. The cap box, lock plate and small caliber places it between say 1820 and 1860. The hardware butt plate, trigger guard and lock look like imports. This is proper to the late period. Gun smith like today ordered ready made parts and produced a rifle.
This rifle from your pictures looks more like a late Southern Mtn Rifle. The low comb and drop of heel to the high breech angle and well curved butt plate. The curved butt plate is to fit the upper bicept of the arm not the shoulder. This allowed the shooter to keep the most of the body mass hidden when shooting.