An asymmetric elastic modulus is a recently discovered and unexpected property of hybrid molecular materials that has significant implications for their underlying thermomechanical reliability. Elastic asymmetries are inherently related to terminal groups in the molecular structure, which limit network connectivity. Terminal groups sterically interact to stiffen the network in compression, while they disconnect the network and interact significantly less in tension. Here we study the importance of terminal group molecular weight and size (OH, methyl, vinyl, and phenyl) on the resulting elastic asymmetries and find that increasing the terminal group size actually leads to even larger degrees of asymmetry. As a result, we develop a molecular design criterion to predict how molecular structure affects the mechanical properties, a vital step toward integrating hybrid molecular materials into emerging nanotechnologies.