Robot-assisted catheterization has garnered a good attention for its potentials in treating cardiovascular diseases. However, advancing surgeon-robot collaboration still requires further research, particularly on task-specific automation. For instance, automated tool segmentation can assist surgeons in visualizing and tracking of endovascular tools during cardiac procedures. While learning-based models have demonstrated state-of-the-art segmentation performances, generating ground-truth labels for fully-supervised methods is both labor-intensive time consuming, and costly. In this study, we propose a weakly-supervised learning method with multi-lateral pseudo labeling for tool segmentation in cardiovascular angiogram datasets. The method utilizes a modified U-Net architecture featuring one encoder and multiple laterally branched decoders. The decoders generate diverse pseudo labels under different perturbations, augmenting available partial labels. The pseudo labels are self-generated using a mixed loss function with shared consistency across the decoders. The weakly-supervised model was trained end-to-end and validated using partially annotated angiogram data from three cardiovascular catheterization procedures. Validation results show that the model could perform closer to fully-supervised models. Also, the proposed weakly-supervised multi-lateral method outperforms three well known methods used for weakly-supervised learning, offering the highest segmentation performance across the three angiogram datasets. Furthermore, numerous ablation studies confirmed the model's consistent performance under different parameters. Finally, the model was applied for tool segmentation in a robot-assisted catheterization experiments. The model enhanced visualization with high connectivity indices for guidewire and catheter, and a mean processing time of 35 ms per frame.