A density functional theory for polymer solutions is generalized to cases where the monomers have a different diameter to the solvent. An appropriate free energy functional is obtained by integration of the generalized Flory equation of state for such systems. This functional predicts that entropic demixing may occur in polymer solutions in which the solvent particles are smaller than the monomers. Demixing is promoted not only by a large size disparity, but also by a high pressure as well as by polymer length. The existence of two separate phases in the bulk solution suggests the possibility of capillary-induced phase transitions, even when the confining surfaces are hard, but otherwise inert. We examine such phase transitions and their relation to surface forces and colloidal stability. The density functional theory also predicts that under certain conditions, layering transitions will occur at hard and flat surfaces. A transition from a thin to a thick polymer-rich surface layer may take place as the separation between two surfaces is decreased, and we study the concomitant change on the surface force. Stable thick phases are predicted even at very large undersaturations, and they give rise to a profound increase of the range and strength of the surface force. We furthermore include comparisons with predictions from a model in which the solvent only enters the description implicitly. Responses of the surface forces to changes in monomer diameter, solvent diameter, polymer density, and chain length are investigated.