Ultrasensitive sensors of various physical properties can be based on percolation systems, e.g., insulating media filled with nearly touching conducting particles. Such a system at its percolation threshold featuring the critical particle concentration, changes drastically its response (electrical conduction, light transmission, etc.) when subjected to an external stimulus. Due to the critical nature of this threshold, a given state at the threshold is typically very unstable. However, stability can be restored without significantly sacrificing the structure sensitivity by forming weak connections between the conducting particles. In this work, we employed nano-bridged nanosphere lithography to produce such a weakly connected percolation system. It consists of two coupled quasi-Babinet complementary arrays, one with weakly connected, and the other with disconnected metallic islands. We demonstrate via experiment and simulation that the physics of this plasmonic system is non-trivial, and leads to the extraordinary optical transmission at narrowly defined peaks sensitive to system parameters, with surface plasmons mediating this process. Thus, our system is a potential candidate for percolation effect based sensor applications. Promising detection schemes could be based on these effects.