This only applies if there's plastic INSTEAD of tissue. In case there's plastic IN ADDITION to tissue, then it makes you heavier, but it still makes you less dense, so you can float better in water.
This logic is flawed. If you stand on some scales and pick up a credit card, the scale will measure you are one credit card heavier. You don't get lighter by adding mass (at least when that mass is also denser then air). And what evidence is there that this plastic in our bodies is additional mass or replaced mass? That is the assumption your logic is based on.
Maybe, but probably not in a noticeable amount that would visibly effect your weight on any scale that isnt accurate to a significat figure only scientists in a lab would care about.