  We have recently shown that normal-metal/superconductor (N/S) bilayer TESs
(superconducting Transition-Edge Sensors) exhibit weak-link behavior.1 Here we
extend our understanding to include TESs with added noise-mitigating
normal-metal structures (N structures). We find TESs with added Au structures
also exhibit weak-link behavior as evidenced by exponential temperature
dependence of the critical current and Josephson-like oscillations of the
critical current with applied magnetic field. We explain our results in terms
of an effect converse to the longitudinal proximity effect (LoPE)1, the lateral
inverse proximity effect (LaiPE), for which the order parameter in the N/S
bilayer is reduced due to the neighboring N structures. Resistance and critical
current measurements are presented as a function of temperature and magnetic
field taken on square Mo/Au bilayer TESs with lengths ranging from 8 to 130
{\mu}m with and without added N structures. We observe the inverse proximity
effect on the bilayer over in-plane distances many tens of microns and find the
transition shifts to lower temperatures scale approximately as the inverse
square of the in- plane N-structure separation distance, without appreciable
broadening of the transition width. We also present evidence for nonequilbrium
superconductivity and estimate a quasiparticle lifetime of 1.8 \times 10-10 s
for the bilayer. The LoPE model is also used to explain the increased
conductivity at temperatures above the bilayer's steep resistive transition.
