We propose a weakly-supervised cell tracking method that can train a convolutional neural network (CNN) by using only the annotation of “cell detection” (i.e., the coordinates of cell positions) without association information, in which cell positions can be easily obtained by nuclear staining. First, we train co-detection CNN that detects cells in successive frames by using weak-labels. Our key assumption is that co-detection CNN implicitly learns association in addition to detection. To obtain the association, we propose a backward-and-forward propagation method that analyzes the correspondence of cell positions in the outputs of co-detection CNN. Experiments demonstrated that the proposed method can associate cells by analyzing co-detection CNN. Even though the method uses only weak supervision, the performance of our method was almost the same as the state-of-the-art supervised method. Code is publicly available in https://github.com/naivete5656/WSCTBFP.