As others have hinted, volume is emerging as being at least as important as weight when computing shipping costs. UPS, USPS, and FedEx all went to volumentric pricing about five years ago.
One more recent development is the USPS’s "Cubic" pricing for parcels under 0.5 cubic feet. This pricing scheme is sort of flat-rate pricing for non-standard-size parcels. Pricing is determined by the dimensions and volume of a parcel, regardless of weight. This won’t help with the OP’s specific issue, but it’s good to keep in mind when shipping smaller but heavier chunks of metal.
In my experience, I’ve found this new pricing tier to be about 10-15% lower than Priority Mail -- which in turn is usually much lower than (sometimes even half that of) equivalent FedEx or UPS 2/3 day services.
But then there’s insurance...