Current multi-view 3D object detection methods often fail to detect objects in the overlap region properly, and the networks' understanding of the scene is often limited to that of a monocular detection network. Moreover, objects in the overlap region are often largely occluded or suffer from deformation due to camera distortion, causing a domain shift. To mitigate this issue, we propose using the following two main modules (1) Stereo Disparity Estimation for Weak Depth Supervision and (2) Adversarial Overlap Region Discriminator. The former utilizes the traditional stereo disparity estimation method to obtain reliable disparity information from the overlap region. Given the disparity estimates as supervision, we propose regularizing the network to fully utilize the geometric potential of binocular images and improve the overall detection accuracy accordingly. Further, the latter module minimizes the representational gap between non-overlap and overlapping regions. We demonstrate the effectiveness of the proposed method with the nuScenes large-scale multi-view 3D object detection data. Our experiments show that our proposed method outperforms current state-of-the-art models, i.e., DETR3D and BEVDet.