Theoretical models of dynamic topography, generated by subducting slabs and consistent with the observed geoid, predict ~1--2 km of subsidence on wavelengths of 102--103 km. The demonstrable existence of such subsidence has important implications for understanding sedimentary basin formation, relative sea level changes, as well as the Earth's viscosity and density structure. Here we present the results of a combined analysis of subsidence data from oceanic marginal basins and their fringing continental shelves. We have chosen to analyze a large area of Southeast Asia where dynamical predictions are believed to be well constrained by the history of subduction. Our joint analysis constrains the maximum amplitude of dynamic subsidence to be ~300 m with a range of 0--500 m, significantly less than predicted. Actively spreading marginal basins have no resolvable dynamic subsidence, but after removing the effects of crustal thickness variation, a few inactive marginal basins are consistently 200--500 m deeper than normal. Adjacent continental sedimentary basins record a possible dynamic subsidence of 0--500 m, although wavelengths are shorter than expected (~102 km). There is also disagreement between the predicted and observed distribution of anomalous subsidence as well as inconsistencies in initiation and duration. These results suggest that mass excess within the mantle, represented by subducted slabs, has little discernible effect on surface topography. Instead, subsidence and marine inundations throughout Southeast Asia are predominantly controlled by lithospheric extension and or by foreland loading. The spatial and temporal distribution of anomalous subsidence suggests that it might not be caused by dynamic topography associated with subducting slabs. A large discrepancy between predicted and observed dynamic topography could be reconciled by changing the density structure of subducted slabs, by supporting mass excess with a marked increase in viscosity at depth, or by decoupling slabs from the surface with a very low viscosity layer.