Variable thickness bridges of superconducting Nb thin films have been fabricated for the first time by a combination of conventional photolithography and scanning force nanofabrication methods. The weak link behavior of these superconducting nanobridges was verified by low-temperature transport measurements, in particular by measuring the critical current as a function of an externally applied magnetic field. Future applications of miniaturized weak link structures may include high-resolution scanning SQUID microscopes.