Bioinks play a fundamental role in skin bioprinting, dictating the printing fidelity, cell response, and function of bioprinted 3D constructs. However, the range of bioinks that support skin cells' function and aid in the bioprinting of 3D skin equivalents with tailorable properties and customized shapes is still limited. In this study, we describe a bioinspired design strategy for bioengineering double crosslinked pectin-based bioinks that recapitulate the mechanical properties and the presentation of cell-adhesive ligands and protease-sensitive domains of the dermal extracellular matrix, supporting the bioprinting of bilayer 3D skin models. Methacrylate-modified pectin was used as a base biomaterial enabling hydrogel formation via either chain-growth or step-growth photopolymerization and providing independent control over bioink rheology, as well as the mechanical and biochemical cues of cell environment. By tuning the concentrations of crosslinker and polymer in bioink formulation, dermal constructs were bioprinted with a physiologically relevant range of stiffnesses that resulted in strikingly site-specific differences in the morphology and spreading of dermal fibroblasts. We also demonstrated that the developed thiol-ene photo-clickable bioinks allow for the bioprinting of skin models of varying shapes that support dermis and epidermis reconstruction. Overall, the engineered bioinks expand the range of printable biomaterials for the extrusion bioprinting of 3D cell-laden hydrogels and provide a versatile platform to study the impact of material cues on cell fate, offering potential for in vitro skin modeling.