High-resolution Hα images of solar filaments show a variety of dark fine-structure fibrils, most of them aligned with the magnetic field that is sheared with respect to the filament long axis. Here we demonstrate how such fibrils can be explained in terms of the magnetic field dips produced by realistic mass loading due to plasma condensation along the top of a magnetic prominence arcade. Our interpretation is supported by (2+1)-dimensional radiation-magnetohydrostatic simulations that predict quantitatively the properties of such condensations that are suspended in the dipped magnetic field.