Do you know the "only" test that would prove this [that the soul has a weight] wrong? Take a animal, which has no soul, and do the same test. If it loses weight upon death, then it is physical. If it don't, then the other test proves there is a soul. I don't know of any scientist brave enough to make such a bold quest for actual truth. Because this test has been out there for how long? And no one, that wants to disprove this, is not smart enough to figure out that a soul-less life test would bring no doubt?
I actually think the test has already been done. But the atheist did not like the out come. So it was never revealed. There is a difference between wanted actual truth, and justification for what one wants to believe.