Complex coacervates formed from oppositely charged biopolymers offer a powerful platform for tunable soft materials with applications ranging from underwater adhesives to biomedical scaffolds. While the effects of polymer chemistry and ionic conditions on coacervate dynamics are well documented, the role of molecular asymmetry, particularly in molecular weight and chain flexibility remains underexplored. In this study, we investigate the salt-dependent viscoelasticity and adhesion of hyaluronic acid (HA)–chitosan (CHI) coacervates, focusing on how symmetry or asymmetry in polymer molecular weight and rigidity affects network formation and mechanical performance. We constructed a library of nine HA–CHI coacervate systems varying systematically in polymer molecular weight combinations, spanning both symmetric (matched Mw) and asymmetric (mismatched Mw) pairs. Using small-amplitude oscillatory shear (SAOS) rheology, van Gurp–Palmen plots, and probe tack adhesion testing, we mapped the influence of salt concentration (0–0.8 M NaCl) on dynamic relaxation, plateau modulus, and adhesive strength. Our results reveal a clear distinction between unentangled and entangled coacervates. Unentangled systems, such as low-MW HA/CHI pairs, display rapid terminal relaxation and obey time–salt superposition (tSS) across a wide frequency window, consistent with models of electrostatically governed relaxation. In contrast, entangled systems exhibit non-universal scaling due to salt-insensitive relaxation mechanisms like chain retraction, hydration shell effects, and topological constraints—particularly pronounced in coacervates with high-MW HA. Interestingly, molecular asymmetry plays a critical role: coacervates with flexible, high-MW CHI and shorter HA chains exhibit strong adhesion and dynamic responsiveness at low salt, but rapidly lose cohesion with increasing ionic strength. In contrast, systems dominated by rigid, high-MW HA maintain mechanical resilience and slower dynamics even under salt stress, though at the cost of reduced interfacial adhesion. Together, these findings provide new insights into the structure–dynamics–adhesion relationship in charged polymer networks and highlight how asymmetric combinations of chain length and flexibility can be strategically used to balance salt responsiveness and mechanical performance. These principles open new pathways for designing bioinspired coacervates for adhesives, drug delivery, and soft tissue engineering.