Anticipating an increasing demand for hybrid double network (DN) hydrogels in biomedicine and biotechnology, this study evaluated the effects of each network on the mechanical and biological properties. Polyethylene glycol (PEG) (meth)acrylate hydrogels with varied monomer molecular weights and architectures (linear vs. 4-arm) were produced with and without an added ionically bonded alginate network and their mechanical properties were characterized using compression testing. The results showed that while some mechanical properties of PEG single network (SN) hydrogels decreased or changed negligibly with increasing molecular weight, the compressive modulus, strength, strain to failure, and toughness of DN hydrogels all significantly increased with increased PEG monomer molecular weight. At a fixed molecular weight (10 kDa), 4-arm PEG SN hydrogels exhibited better overall mechanical performance; however, this benefit was diminished for the corresponding DN hydrogels with comparable strength and toughness and lower strain to failure for the 4-arm case. Regardless of the PEG monomer structure, the alginate network made a relatively larger contribution to the overall DN mechanical properties when the covalent PEG network was looser with a larger mesh size (e.g., for larger monomer molecular weight and/or linear architecture) which presumably enabled more ionic crosslinking. Considering the biological performance, adipose derived stem cell cultures demonstrated monotonically increasing cell area and Yes-associated protein related mechanosensing with increasing amounts of alginate from 0 to 2 wt.%, demonstrating the possibility for using DN hydrogels in guiding musculoskeletal differentiation. These findings will be useful to design suitable hydrogels with controllable mechanical and biological properties for mechanically demanding applications. Statement of significance: Hydrogels are widely used in commercial applications, and recently developed hybrid double network hydrogels have enhanced strength and toughness that will enable further expansion into more mechanically demanding applications (e.g., medical implants, etc.). The significance of this work is that it uncovers some key principles regarding monomer molecular weight, architecture, and concentration for developing strong and tough hybrid double network hydrogels that would not be predicted from their single network counterparts or a linear combination of the two networks. Additionally, novel insight is given into the biological performance of hybrid double network hydrogels in the presence of adipose derived stem cell cultures which suggests new scope for using double network hydrogels in guiding musculoskeletal differentiation.