Excellent point.

I suspect you're basically correct, but I would not take the stats results at face value. There are many possible problems resulting from the physical and electrical properties of the scale you're using, that I would not expect to be well behaved in a stats sense. In particular: quantization errors, non-linearity / non-monotonicity of the scale A/D converter (depends strongly on type of A/D used), temperature dependence of both the scale strain gauges and A/D, etc.

The general rule here is that trying to get too many more bits of precision out of a measuring device than it is intended to provide is tricky.

You could calibrate the scale in a number of ways; easiest would probably be to check that it gives consistent readings over time for a fixed weight that's not too small compared to you. You could simply weigh the fixed weight, or you could weigh you and (you + weight).