Tissue engineering and regenerative medicine are confronted with a persistent challenge: the urgent demand for robust, load-bearing, and biocompatible scaffolds that can effectively endure substantial deformation. Given that inadequate mechanical performance is typically rooted in structural deficiencies─specifically, the absence of energy dissipation mechanisms and network uniformity─a crucial step toward solving this problem is generating synthetic approaches that enable exquisite control over network architecture. This work systematically explores structure-property relationships in poly(ethylene glycol)-based hydrogels constructed utilizing thiol-yne chemistry. We systematically vary polymer concentration, constituent molar mass, and cross-linking protocols to understand the impact of architecture on hydrogel mechanical properties. The network architecture was resolved within the molecular model of Rubinstein-Panyukov to obtain the densities of chemical cross-links and entanglements. We employed both nucleophilic and radical pathways, uncovering notable differences in mechanical response, which highlight a remarkable degree of versatility achievable by tuning readily accessible parameters. Our approach yielded hydrogels with good cell viability and remarkably robust tensile and compression profiles. Finally, the hydrogels are shown to be amenable to advanced processing techniques by demonstrating injection- and extrusion-based 3D printing. Tuning the mechanism and network regularity during the cell-compatible formation of hydrogels is an emerging strategy to control the properties and processability of hydrogel biomaterials by making simple and rational design choices.