The effects of film thickness on the columnar packing structure of discotic supramolecules in a thin supported film have been investigated by grazing-incidence small-angle X-ray scattering technique using magnetically aligned cobalt octa(n-decylthio)porphyrazine (CoS10) films on octadecyltrichlorosilane (OTS)-functionalized substrates as model systems. Magnetically aligned CoS10 films with a range of film thicknesses (49-845 nm) form uniaxially oriented 'edge-on' columnar superstructures with their columnar directors perpendicular to the applied magnetic field. However, the orientational ordering of the columnar packing in the plane perpendicular to the applied magnetic field is strongly dependent on the film thickness. While being damped by the elasticity of the side chains of CoS10, the strong interfacial interaction at the film-substrate interface propagates up to 50-100 nm from the substrate, maintaining the orientation of columnar packing in the plane perpendicular to the applied magnetic field. When the distance from the film-substrate interface becomes larger than about 100 nm, symmetric tilting of columnar layer orientation, which saturates at 11.5 degrees , occurs due to longitudinal edge dislocations induced by accumulated elastic deformation.