Organosilicate glasses (OSG) are of great technological interest as low-k dielectrics. We use ab initio simulations to analyze the influence of the C/Si ratio in OSG on the density and elastic properties of pore-free material to gain a detailed understanding of the origins of these properties in this class of materials. We find that the addition of carbon to amorphous silica leads to a stiffening of the material by removing the bending degrees of freedom of Si-O-Si bonds. This transition in mechanisms of stiffness, leads to a distinctly nonlinear behavior of the bulk and elastic modulus over the C/Si ratio. Experimental results do not contradict our findings, however dominant pore effects impede conclusive comparison.