  A study of the double logarithmic in the center-of-mass energy, $s$,
contributions to the four-graviton scattering amplitude is presented for
four-dimensional ${\cal N} \geq 4$ supergravities. This includes a novel
representation for the coefficients of the perturbative expansion based on
exactly solvable recurrences. A review is given of the structure in the complex
angular momentum plane for the $t$-channel partial wave singularities of the
different amplitudes. Working in impact parameter representation, $\rho$, it is
shown that the resummation of double logarithms makes gravity weaker in regions
of small $\rho$ and large $s$. This screening of the gravitational interaction
at short distances in the double logarithmic sector of the amplitudes is more
acute as the number of gravitinos in the theory increases. It brings
corrections to the eikonal phase which can change the sign of the graviton's
deflection angle and generate regions with repulsive interaction. For very
small impact parameters there appears a constant negative shift in both the
eikonal phase and Shapiro's time delay which is not large enough to generate
causality violation.
