Localized zones of high-amplitude, discontinuous seismic reflections 100 km off the coast of Massachusetts, USA, have P wave velocities up to 190 m/s lower than those of adjacent sediments of equal depth (250 m below the sea floor). To investigate the origin of these low-velocity zones, we compare the detailed velocity structure across high-amplitude regions to adjacent, undisturbed regions through full-waveform inversion. We relate the full-waveform inversion velocities to effective stress and overpressure with a power law model. This model predicts localized overpressures up to 2.2 MPa associated with the high-amplitude reflections. To help understand the overpressure source, we model overpressure due to erosion, glacial loading, and sedimentation in one dimension. The modeling results show that ice loading from a late Pleistocene glaciation, ice loading from the Last Glacial Maximum, and rapid sedimentation contributed to the overpressure. Localized overpressure, however, is likely the result of focused fluid flow through a high-permeability layer below the region characterized by the high-amplitude reflections. These high overpressures may have also caused localized sediment deformation. Our forward models predict maximum overpressure during the Last Glacial Maximum due to loading by glaciers and rapid sedimentation, but these overpressures are dissipating in the modern, low sedimentation rate environment. This has important implications for our understanding continental shelf morphology, fluid flow, and submarine groundwater discharge off Massachusetts, as we show a mechanism related to Pleistocene ice sheets that may have created regions of anomalously high overpressure.