Bridge weigh-in-motion (BWIM) is a technique for detecting heavy vehicles that may cause serious damage to real bridges. BWIM is realized by analyzing the strain signals observed at places on the bridge in terms of bridge-component responses to the axle loads. In current practice, a BWIM system requires multiple strain sensors to collect vehicle properties including speed and axle positions for accurate load estimation, which may limit the system’s life-span. Furthermore, BWIM should consider a wide variety of waveforms, which may be caused by vehicle acceleration and/or the various traveling positions in lanes. In this paper, we propose a novel BWIM mechanism, which employs a deep convolutional neural network (CNN). The CNN is able to learn actual traffic conditions and achieve accurate load estimation by using only a single strain sensor. The training dataset is collected from a distant load meter, by consulting traffic surveillance cameras and identifying similar vehicles. After the system initialization, the CNN requires no additional sensors (or cameras) for axle detection, which may reduce the costs of both installation and system maintenance.