In this talk I will describe constraints from causality and unitarity on 2→2 graviton scattering in weakly-coupled gravitational effective field theories. Together, causality and unitarity imply dispersion relations that connect low-energy observables to high-energy data. Using such dispersion relations, we can derive two-sided bounds on gravitational Wilson coefficients in terms of the mass M of new higher-spin states. Our bounds imply that gravitational interactions must shut off uniformly in the limit G→0, and prove the scaling with M expected from dimensional analysis. In addition they demonstrate the gravity must be weakly coupled at all scales below Planck.