Large-scale folding of sedimentary rock is generally considered to be a response to horizontal tectonic shortening. We test an alternative hypothesis where we propose that in basins with high sedimentation rates where folds are cored by mechanically weak mobile shale, fold growth can be amplified by the gravitational loading of the weak underlying shale. We use two-dimensional plane-strain, finite element code to investigate the mechanics of growth of a shale-cored fold in the South Caspian Sea Basin, where c.10 km of sediment was deposited in the last 6 My. The overburden and syn-kinematic sediments are modelled as poro-elastoplastic materials using a modified Cam-Clay critical state model and the mobile shale is modelled as visco-plastic Herschell-Bulkley material, representative of conditions at critical state. The results show that the atypical geometries of the fold strata can be explained by the application of horizontal shortening and simultaneous sediment loading of the visco-plastic layer. The viscosity of the shale determines whether differential loading will cause fold growth and its density controls the magnitude of fold amplification, with a lower density causing greater fold amplification. Results demonstrate that the magnitude of shale inflation is controlled by complex interaction of the relative amounts of shortening and sedimentation rate.