  We propose a new method for probing the time variation of the effective
Newton's constant $G_{\rm eff}$, based on the optimal redshift weighting
scheme, and demonstrate the efficacy using the DESI galaxy spectroscopic
survey. We find that with the optimal redshift weights, the evolution of
$G_{\rm eff}(z)$ can be significantly better measured: the uncertainty of
$G_{\rm eff}(z)$ can be reduced by a factor of $2.2\sim12.8$ using the DESI BGS
sample at $z \lesssim0.45$, and by a factor of $1.3\sim4.4$ using the DESI ELG
sample covering $0.65\lesssim z\lesssim1.65$.

Cosmology and Nongalactic Astrophysics