Weak link behavior in transition-edge sensor (TES) microcalorimeters creates the need for a more careful characterization of a device's thermal characteristics through its transition. This is particularly true for small TESs where a small change in the bias current results in large changes in effective transition temperature. To correctly interpret measurements, especially complex impedance, it is crucial to know the temperature-dependent thermal conductance, G(T), and heat capacity, C(T), at each point through the transition. We present data illustrating these effects and discuss how we overcome the challenges that are present in accurately determining G and T from I-V curves. We also show how these weak link effects vary wi.th TES size. Additionally, we use this improVed understanding of G(T) to determine that, for these TES microcalorimeters. Kaptiza boundary resistance dominates the G of devices with absorbers while the electron-phonon coupling also needs to be considered when determining G for devices without absorber