Climate change could potentially destabilize marine ice sheets, which would affect projections of future sea-level rise1, 2, 3, 4. Specifically, an instability mechanism5, 6, 7, 8 has been predicted for marine ice sheets such as the West Antarctic ice sheet that rest on reversed bed slopes, whereby ice-sheet thinning or rising sea level leads to irreversible retreat of the grounding line. However, existing analyses of this instability mechanism have not accounted for deformational and gravitational effects that lead to a sea-level fall at the margin of a rapidly shrinking ice sheet9, 10, 11. Here we present a suite of predictions of gravitationally self-consistent sea-level change following grounding-line migration. Our predictions vary the initial ice-sheet size and also consider the contribution to sea-level change from various subregions of the simulated ice sheet. Using these results, we revisit a canonical analysis of marine-ice-sheet stability5 and demonstrate that gravity and deformation-induced sea-level changes local to the grounding line contribute a stabilizing influence on ice sheets grounded on reversed bed slopes. We conclude that accurate treatments of sea-level change should be incorporated into analyses of past and future marine-ice-sheet dynamics.