  We explore a re-parameterization of the lensing amplitude tension between
weak lensing (WL) and cosmic microwave background (CMB) data and its
implications for a joint resolution with the Hubble tension. Specifically, we
focus on the lensing amplitude over a scale of 12 Mpc in absolute distance
units using a derived parameter $S_{12}$ and show its constraints from recent
surveys in comparison with Planck 2018. In WL alone, we find that the absolute
distance convention correlates $S_{12}$ with $H_0$. Accounting for this
correlation in the 3D space $S_{12}\times \omega_m \times h$ reproduces the
usual levels of $2\sim 3\sigma$ tension inferred from $S_8\times\Omega_m$.
Additionally, we derive scaling relations in the $S_8\times h$ and
$S_{12}\times h$ planes that are allowed by $\Lambda$CDM and extrapolate target
scalings needed to solve the $H_0$ and lensing-amplitude tensions jointly in a
hypothetical beyond-$\Lambda$CDM model. As a test example, we quantify how the
early dark energy scenario compares with these target scalings. Useful fitting
formulae for $S_8$ and $S_{12}$ as a function of other cosmological parameters
in $\Lambda$CDM are provided, with 1% precision.
