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We consider weak gravity at accelerations $\alpha<a_H$ when Rindler andcosmological horizon collude at $R_H=c/H$, where $c$ is the velocity of lightand $H$ is the Hubble parameter. This is manifest in reduced inertia $m$, belowthe value $m_0$ in Newtonian gravity. Striking evidence for a sharp transitionto weak gravity is found in galaxy rotation curves. Their sensitivity to thecosmological background is expressed by correlations to the decelerationparameter $q=1-(4\pi a_0/cH)^{2}$ and $q=-1/2 -3(\Omega_b/\sqrt{2}\sqrt{\pi})^{1/2}$, where $a_0$ is Milgrom's scale in thebaryonic Tully-Fisher relation of spiral galaxies and $\Omega_b$ is thebaryonic matter density. The Planck value $\Omega_b=0.048$ with $H\simeq 73$ kms$^{-1}$ Mpc$^{-1}$ shows $q\simeq-0.85$. Future surveys may determine$Q_0=\left.dq(z)/dz\right|_{z=0}$ to provide a direct test for dynamical darkenergy ($Q_0>2.5$) versus $\Lambda$CDM ($Q_0<1$).

New estimates of the deceleration parameter in weak gravity