We show that the size of silica nanoparticles influences the nature of their aggregation in an aqueous solution of a relatively hydrophobic nonionic surfactant, C12E4. We present results for dispersions of silica nanopartides with sizes varying from 8 to 26 nm, in a 75: 25 C12E4/water system, that forms a lamellar phase, L-alpha, at room temperature. Addition of silica particles does not affect the formation of the L-alpha phase. Nanoparticles smaller than about 11 nm aggregate irreversibly in the C12E4/water system. However, nanoparticles larger than about 15 nm aggregate in the L-alpha phase, but are dispersed at temperatures above the L-alpha order-disorder temperature. Thus, in contrast to the smaller particles, aggregation of silica nanopartides larger than about 15 nm is reversible with temperature. We use small-angle neutron scattering (SANS) demonstrate that these results can be explained by the size-dependent wrapping of nanoparticles by surfactant bilayers. Larger particles, above 15 nm in size, are sterically stabilized by the formation of an adsorbed surfactant bilayer. The cost of bilayer bending inhibits adsorption onto the highly curved surfaces of smaller particles, and these ``bare'' particles aggregate irreversibly.