the 6 1 stamped on the barrel flats is the Unstruck barrel weight. Actual finished barrel weight differs very slightly.

Wow! That looks to be a great gun with very few flaws given it's age, plus a neat old case and cleaning kit, and a family heirloom to boot! Don't be afraid to shoot it, the old 10's are a blast, I have a similiar gun and use it a lot. Do you hunt waterfowl or turkey, that would be a great gun for it. As Bill said the wood repair could be improved to be invisible or near invisible and the screws can be cleaned up or replaced. Go through the reloading forum on this website there is lots of information on the 2 7/8" 10ga. If you want to get into reloading for this gun shoot me a PM anytime and I'll walk you through it. Have fun!

I am sure the 6# weight he mentioned is just the barrels.
Overall the gun is a pretty good shape. Yeah, the floorplate screws are buggared up, but the rest look pretty nice.