This would only be relevant if you were accelerating relative to the Earth. The scale measures the normal force keeping you at rest relative to the Earth's center; the force being exerted on the Earth does not change that. (Modulo the orbital-velocity argument, which I'll respond to separately.)
This is our monthly thread for collecting these little gems and pearls of wisdom, rationality-related quotes you've seen recently, or had stored in your quotesfile for ages, and which might be handy to link to in one of our discussions.