Superconducting transition-edge sensors (TESs) are highly sensitive detectors. Based on the outstanding performance on spectral resolution, the X-ray integral field unit (X-IFU) instrument on-board athena will be equipped with a large array of TES-based microcalorimeters. For optimal performance in terms of the energy resolution, it is essential to limit undesirable nonlinearity effects in the TES detector. Weak-link behavior induced on the TES by superconducting leads is such a nonlinearity effect. We designed and fabricated smart test structures to study the effect of the superconducting leads on the intrinsic transition curve of our TiAu-based TES bilayer. We measured and analyzed the resistance versus temperature transition curves of the test structures. We found relations of long-distance proximity effects with TES length and different lead materials. Based on these results, we can redesign and further optimize our TES-based X-ray detectors.