This paper introduces a novel nothing-on-road (NOR) bridge weigh-in-motion (BWIM) approach with deep learning (DL) and non-invasive ground-based radar (GBR) time-series data. BWIMs allow site-specific structural health monitoring (SHM) but are usually difficult to attach and maintain. GBR measures the bridge deflection contactless. In this study, GBR and an unmanned aerial vehicle (UAV) monitor a two-span bridge in Germany to gather ground-truth data. Based on the UAV data, we determine vehicle type, lane, locus, speed, axle count, and axle spacing for single-presence vehicle crossings. Since displacement is a global response, using peak detection like conventional strain-based BWIMs is challenging. Therefore, we investigate data-driven machine learning approaches to extract the vehicle configurations directly from the displacement data. Despite a small and imbalanced real-world dataset, the proposed approaches classify, e.g., the axle count for trucks with a balanced accuracy of 76.7% satisfyingly. Additionally, we demonstrate that, for the selected bridge, high-frequency vibrations can coincide with axles crossing the junction between the street and the bridge. We evaluate whether filtering approaches via bandpass filtering or wavelet transform can be exploited for axle count and axle spacing identification. Overall, we can show that GBR is a serious contender for BWIM systems.