Go to any smoke shop. They sell jewelers scales. Cheap. Perfect for weighing coins. But I also say your coin is fake.
Doubtful. American Silver Eagles (ASE's) are supposed to contain 1 oz of 999 silver. Un-like a coin that was produced for regular circulation and carries a premium that a collector would pay (extrinsic value) most ASE's don't have a lot of value above the price of silver. (intrinsic value) So to counterfeit a low value coin using genuine silver would not be very profitable. ie use $24 worth of silver to make a counterfeit $38 coin, not smart. Use $20 of silver + .50 of tin and make a $200 counterfeit Morgan dollar, smart. Not very nice but smart.
Counterfeit, likely from China. The letterings not right and the rim isn't right. Date looks wrong. Not a mint product.
The sun's ray under the gown, the details of the sandals and the overall cast look are the tells of a counterfeit for me.