Many new made sxs shotguns use pretty short barrels, this by itself helps keep the overall weight down.
Many of the older double barreled guns had quite long barrels. But, because they were double barreled they could also be quite heavy compared to single barreled/single locked guns of the same type.
So, the stocks were made quite thin and light to help reduce the overall weight issues.
This thin stock carries over into the cowboy time period and age.
Just some thoughts, and perhaps an explanation?
My best,
Blair