Experiments took place on this, but the results are not very scientific. In fact the experiments are almost the definition of pseudoscience (something "portrayed as scientific but diverges from the required standards for scientific work").

If you sit a dying man on a scale and measure their weight at their time of death, you will see a drop. But, if you sit a healthy man on a scale and measure their weight while they think about ice-cream, you will see their weight drop as well.

I'm not saying this proves their isn't a soul, or that a soul doesn't have weight, or anything like that. There just isn't any scientific proof one way or another.