Of what value to the owner is the barrel weight stamp?
That weight stamp was most likely intended for the Fox worker who went to fetch a set of barrels to make up a gun in a specified weight range. Seems if it were important for the owner to know, the Fox company would have made it a point to restamp the many (majority?) barrels that have no numbers.
You have the gun, you know the weight and the handling characteristics. Why work backward in an effort to speculate on which bin the barrels came out of? How is that information helpful?