  Using the recent model-independent determination of the charge-weak form
factor difference $\Delta F_{\rm CW}$ in $^{48}$Ca and $^{208}$Pb by the CREX
and PREX-2 collaborations together with some well-determined properties of
doubly magic nuclei, we perform Bayesian inference of the symmetry energy
$E_{\rm sym}(\rho)$ and the neutron skin thickness $\Delta r_{\rm np}$ of
$^{48}$Ca and $^{208}$Pb within the Skyrme energy density functional (EDF). We
find the inferred $E_{\rm sym}(\rho)$ and $\Delta r_{\rm np}$ separately from
CREX and PREX-2 are compatible with each other at $90\%$ C.L., although they
are inconsistent at $68.3\%$ C.L. with CREX (PREX-2) favoring a very soft
(stiff) $E_{\rm sym}(\rho)$ and rather small (large) $\Delta r_{\rm np}$. By
combining the CREX and PREX-2 data, we obtain a soft symmetry energy around
saturation density $\rho_0$ and thinner $\Delta r_{\rm np}$ of $^{48}$Ca and
$^{208}$Pb, which are found to be closer to the corresponding results from CREX
alone, implying the PREX-2 is less effective to constrain the $E_{\rm
sym}(\rho)$ and $\Delta r_{\rm np}$ due to its lower precision of $\Delta
F_{\rm CW}$. Furthermore, we find the Skyrme EDF results inferred by combining
the CREX and PREX-2 data nicely agree with the measured dipole polarizabilities
$\alpha_D$ in $^{48}$Ca and $^{208}$Pb as well as the neutron matter equation
of state from microscopic calculations. The implications of the inferred soft
$E_{\rm sym}(\rho)$ around $\rho_0$ are discussed.
