Could a small piece of conductive foam or some cleverly layered tin foil+paper work? So put the object on the shim (which has a known or even negligeable weight)
I once put some aluminum duct tape completely over the touch pad of an old laptop to see what would happen. Turns out it induced enough "eddy currents" to make the mouse move around the screen without me touching it--in a way, visualizing the currents!
I connected the foil to ground using a small strip of the tape to the ground metal of a USB port on the side and it disabled the touch pad.
If you ever want to do this keep in mind to reconfigure the mouse as a digital pointing device (tablet like), otherwise the mouse acceleration will mess up your position measurement.