It turns out that the only source for the 21 gram figure is a discredited study carried out in 1907 by a Haverhill, Massachusetts, doctor by the name of Duncan MacDougall. He managed (apparently overcoming any ethical qualms over human experimentation) to put six dying people on a bed equipped with sensitive springs, and claimed to have observed a sudden loss of weight – about ¾ of an ounce – at the exact moment of their death. Having reasoned that such loss could not be explained by bowel movements or evaporation, he concluded he must have measured the weight of the soul. A follow-up experiment also showed that dogs (which were healthy, so they were probably poisoned on purpose by the good doctor) don't seem to suffer the same sort of loss, therefore they don't have souls (sorry, you canine lovers).
This is an excellent example of where pseudoscience and belief go wrong, on a variety of levels. Let us start with MacDougall's claim itself: it turns out that his data were decidedly unreliable by any decent scientific standard. Not only was the experiment never repeated (by either MaDougall or anyone else), but his own notes (published in American Medicine in March 1907) show that of the six data points, two had to be discarded as “of no value”; two recorded a weight drop, followed by additional losses later on (was the soul leaving bit by bit?); one showed a reversal of the loss, then another loss (the soul couldn't make up its mind, leaving, re-entering, then leaving for good); and only one case actually constitutes the basis of the legendary estimate of ¾ of an ounce. With data like these, it's a miracle the paper got published in the first place.
Second, as was pointed out immediately by Dr. Augustus P. Clarke in a rebuttal also published in American Medicine, MacDougall failed to consider another obvious hypothesis: that the weight loss (assuming it was real) was due to evaporation caused by the sudden rise in body temperature that occurs when the blood circulation stops and the blood can no longer be air-cooled by the lungs. This also elegantly explains why the dogs showed no weight loss: as is well known, they cool themselves by panting, not sweating like humans do.
Third, MacDougall's allegedly inescapable conclusion (“How other shall we explain it?”) did not derive from any theory of the soul, but was simply arrived at by excluding a small number of other possibilities. In other words, the soul “explanation” won by default, without having to go through the onerous process of positive confirmation. This is yet another version of the “god-of-the-gaps” argument so in vogue among the faithful, and that constitutes the backbone – such as it is – of Intelligent Design “theory.”
But perhaps most damning of all is the very idea that the soul has weight. Whatever it is, the soul since Plato's time has been understood as immaterial, i.e. without mass and, therefore, weightless. Obviously, this in turn raises all the classic problems of dualism: how can something immaterial interact with a material world? How can ghosts walk through walls and yet “see” things or make noises? How can the mind direct our actions – that famous conundrum that stymied Descartes – if it is an incorporeal “substance” (itself an oxymoron)?
Even more basically: why are the so-called “faithful” perennially in search of scientific confirmation of their inanities? Shouldn't faith be enough? Indeed, isn't the very idea of faith as a value that one should hold fast to it, not only despite the lack of evidence, but even in the face of contrary evidence? C'mon guys, I'm beginning to think that somewhere in your subconscious you have this terrifying suspicion that you really believe in nonsense, and are therefore desperate to get science to provide some evidence, however flimsy, that you are right after all. Why not shed the superstition altogether and see what happens? It's a nice, comprehensible world out here.