No, because it pulls you, your scale and the Earth all (very close to) equally.
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.