<p>Nanoscale molecular transport governs mass diffusion and responsiveness in soft porous crystals, where guest adsorption induces host deformation and alters rigidity. Surface-mediated adsorption generates inhomogeneous adsorbate distributions, leading to spatial variations in stiffness—elastic heterogeneity—whose role in adsorption kinetics remains poorly understood. Here, we show that elastic heterogeneity governs adsorption kinetics, giving rise to size-dependent uptake, surface creasing, and anomalous dynamic scaling distinct from established scaling laws. Stress relaxation near corners accelerates adsorption, while on surfaces, creases emerge at flexible unadsorbed regions compressed between rigid adsorbed domains. The resulting lateral correlations of adsorbates exhibit a breakdown of scale invariance between global and local fluctuations. These findings provide a mechanistic foundation for controlling adsorption and deformation kinetics via elastic heterogeneity. Our work opens a route to engineering responsive materials, where mechanical feedback is harnessed to control cooperative molecular transport and drive macroscopic shape changes under external perturbations.</p><p></p>