The weight of a Model 1874 Sharps is entirely dependent upon how it is configured. About the lightest I have ever seen is around ten pounds, the heaviest around 22 pounds. Their average weight is probably around 12 pounds. Here are two of mine that illustrate the range that most will fall within. The upper is my long range match rifle in .45-2.6" (aka ".45-100"), which has a 34" #1 heavy full octagon barrel. It weighs over 14 pounds. The lower is one of my hunting rifles in .45-2.4" (aka ".45-90"), built as light as possible. It has a 28" half octagon half round barrel in the standard weight, coming in at just about ten pounds.
Also typical for the era (late 19th century) is my original Ballard Pacific in .45-70, sporting a #1 heavy tapered octagon barrel in a 32" length. It goes about 12 pounds.
Then again, I have a first year Winchester Highwall in .40-70 Sharps Straight that only goes about eight pounds with a standard weight 32" half octagon half round barrel.
So, like today, rifles were all over the map back then. They did, generally, put up with a bit more rifle weight than we like to today. In light of that, an 11 pound Hawken was not out of line. They were, however, carried far more often in saddle scabbards and on wagon seats than by hand, on foot. Eastern rifles tended to be lighter, because their owners were more apt to be still hunting their game in thick woods. Not many did that out West, and they wanted greater power and range, so they accepted that their rifles had to be bigger and heavier.