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Very light, really. If you look at the second pic, you can see the inside of the scales. They are stamped from a thin sheet of silver and then put together.
They do look heavy, I agree!

This set of sterling scales was made by J.F. Fradley of New York, New York, 1866-1936. Seems to be turn of century. I found a blade in this Fredrick Reynolds which seemed to fit properly. Lots of...