The de Sitter transition scale $a_{dS}=cH$ to anomalous galaxy dynamics was previously derived from first principles based on the background Hubble expansion $H$ and the velocity of light $c$, and shown to be in tension with $\Lambda$CDM galaxy simulations. Tracing late-time cosmology, it predicted the deep-asymptotic acceleration scale $a_0^{th}\simeq 1.66\times 10^{-8}{\rm cm\,s^{-2}}$ without adjustable parameters based on $H$ and the deceleration parameter $q$. A recent weak-lensing determination of $a_0^{WL} = 1.63_{-0.20}^{+0.23}\times 10^{-8}{\rm cm\,s}^{-2}$ now provides an independent empirical test of this prediction. The agreement with the updated theoretical value $a_0^{th} = 1.63_{-0.14}^{+0.13}\times 10^{-8}{\rm cm\,s^{-2}}$ closes the logical chain between cosmology, galaxy dynamics, and asymptotic scaling. Unlike phenomenological fits to rotation curves, this result does not rely on tuning or baryonic modeling but follows directly from background cosmology. This parameter-free model suggests some further tests by galaxy surveys extending over a finite range of redshifts.