Ubiquitous in most superconducting materials and a common result of nanofabrication processes, weak links are known for their limiting effects on the transport of electric currents. Still, they are at the root of key features of superconducting technology. By performing quantitative magneto-optical imaging experiments and thermomagnetic model simulations, we correlate the existence of local maxima in the magnetization loops of focused ion beam (FIB)-patterned Nb films to a magnetic field induced weak-to-strong-link transformation increasing their critical current. This phenomenon arises from the nanoscale interaction between quantized magnetic flux lines and FIB-induced modifications of the device microstructure. Under an ac drive field, this leads to a rectified vortex motion along the weak link. The reported tunable effect can be exploited in the development of new superconducting electronic devices, such as flux pumps and valves, to attenuate or amplify the supercurrent through a circuit element and as a strategy to enhance the critical current in weak-link-bearing devices.