The Gravity Lineations Intraplate Melting Petrologic and Seismic Expedition (GLIMPSE) Experiment investigated the formation of a series of non--hot spot, intraplate volcanic ridges in the South Pacific and their relationship to cross-grain gravity lineaments detected by satellite altimetry. Using shipboard gravity measurements and a simple model of surface loading of a thin elastic plate, we estimate effective elastic thicknesses ranging from ~2 km beneath the Sojourn Ridge to a maximum of 10 km beneath the Southern Cross Seamount. These elastic thicknesses are lower than predicted for the 3--9 Ma seafloor on which the volcanoes lie, perhaps due to reheating and thinning of the plate during emplacement. Anomalously low apparent densities estimated for the Matua and Southern Cross seamounts of 2050 and 2250 kg m-3, respectively, probably are artifacts caused by the assumption of only surface loading, ignoring the presence of subsurface loading in the form of underplated crust and/or low-density mantle. Using satellite free-air gravity and shipboard bathymetry, we calculate the age-detrended, residual mantle Bouguer anomaly (rMBA). The rMBA corrects the free-air anomaly for the direct effects of topography, including the thickening of the crust beneath the seamounts and volcanic ridges due to surface loading of the volcanic edifices. There are broad, negative rMBA anomalies along the Sojourn and Brown ridges and the Hotu Matua seamount chain that extend nearly to the East Pacific Rise. These negative rMBA anomalies connect to negative free-air anomalies in the western part of the study area that have been recognized previously as the beginnings of the cross-grain gravity lineaments. Subtracting the topographic effects of surface loading by the ridges and seamounts from the observed topography reveals that the ridges are built on broad bands of anomalously elevated seafloor. This swell topography and the negative rMBA anomalies contradict the predictions of lithospheric cracking models for the origin of gravity lineaments and associated volcanic ridges, favoring models with a dynamic mantle component such as small-scale convection or channelized asthenospheric return flow.