Load the frame on a trailer. Take the tow vehicle, trailer, and frame to public scales, scrap dealer, truck stop, etc.. Weigh everything. Pull off the scales and unload the frame.. Re-weigh the tow vehicle and empty trailer.. Subtract this weight from the first weight, that's the weight of the frame.. Detective McClaine used this same deductive reasoning when computing how to wind up with 3 gallons of water in a 5 gallon jug..
If the plating facility charges by weight, why can't they weigh the frame????