Just been asked to take a look at this thread and comment.
Measure the walls allover their surfaces. Check for thickness and even distribution of metal. a gradually tapering thin spot of 16 thou well down the length will in all likelihood be fine for normal use, as long as no further problems occur, like dents.
Other posters are correct. There is no proof requirement for a barrel wall thickness. If it is in-proof, it is in proof. This is down to the bore measurement 9" from the breech being within 10 thou of the last proof test and stamp (8 thou if it is metric).
How did a dealer sell it to him? Well, it is in proof and he showed it to him and he bought it. Buyer bbeware if all else is legal. Buying an old gun is like buying an old car - do your homework.
The thin barels will make it less valuable and harder to sell. Sleeving will not be economical. It sounds like you have a first model Royal from the mid 1880s - 1890 period.
Teague liningh will cost £1500 - also not likely to be recovered in asubsequent sale. Sell it as it is if you are tired of it and find abuyer who understands and accepts its limitations. Unfortunately, this will be reflected in the price they will pay.
Hopefully it was reflectyed in the price you paid
