I have a #3 in 45-70 I have never weighed it but is listed at 6lb, then add a scope, which weigh about 16oz give or take a couple and rings and bases and you are right about 7.5lb. I would not trust a bath room scale at the low end, since the are designed to weigh people which in my guess would be between 120 to 220lb and most scales max out at 250 or 260 lb. I would use a scale that is more designed for 0-25lb. Do you have a lumber yard that sells nails and screws by the pound that has a scale to measure them? Usually those old style are also have a balance beam adjustment on them.
I have no idea how much more a #1 is listed at but the only difference in those 2 is the stock, and the breech lever, so it is very possible depending on the scope they would weigh the same. Then add in the unaccuracy of the bathroom scale at that range and to weigh down to ounces, I would say you are just getting a close guess to the comparison weight. Just because you have a digital scale means nothing in its accuracy, it just has a digital read out instead of a dial and needle.