You’re assuming the Newtonian theory of gravity, the parent poster uses Einstein’s general relativity. These theories disagree on quite a lot; e.g. general rela

You’re assuming the Newtonian theory of gravity, the parent poster uses Einstein’s general relativity. These theories disagree on quite a lot; e.g. general relativity predicts that light is affected by gravity, while Newton’s theory would not since photons are massless particles. Einstein was proven right here too. Note however that the quoted effect – difference in weight between a compressed and uncompressed spring – will realistically be so small that I doubt you could measure that in a lab. To get a sense of how small that effect is, try comparing the E=mc^2 mass-energy of a spring to its E=kx^2 compression energy...