In George Washington's days, there were no cameras. One's image was either sculpted or painted. Some paintings of George Washington showed him standing behind a desk with one arm behind his back while others showed both legs and both arms.
Prices charged by painters were not based on how many people were to be painted, but by how many limbs were to be painted. Arms and legs are "limbs;" therefore painting them would cost the buyer more.
Hence the expression, "Okay, but it'll cost you an arm and a leg."