Cryogenic transmission electron microscopy (cryo-TEM) and small angle neutron scattering (SANS) are used to investigate the association of amphiphilic polymers consisting of a double-chain hydrophobic tail attached onto poly(ethylene glycol) (PEG) polymer chains into two different systems of equilibrium vesicles. For cetyltrimethylammonium bromide (CTAB)/sodium perfluorohexanoate (FC5) vesicle bilayers, the size distribution of the vesicles slightly becomes narrow in the presence of the polymers, suggesting that the wedge-shaped polymers increase the spontaneous curvature of the vesicles. In contrast, the confinement of polymer molecules inside the CTAB/sodium perfluorooctanoate (FC7) vesicles that are stabilized by spontaneous curvature causes an abrupt decrease in the bilayer rigidity. By an analysis of vesicle size distribution, it is found that the membrane elasticity of CTAB/FC7 vesicles is varied considerably from 6k(B)T to 0.3k(B)T, implying the transition of stabilization mechanism from spontaneous curvature to thermal fluctuation in the presence of polymer. The polymer incorporation mechanism into the bilayers is understood, in the comparison of the vesicle radius and size distribution before and after adding polymer, as that the polymer is anchored into the vesicle bilayer owing to hydrophobic property after the adsorption on the surface of the bilayer.