Weakly supervised object localization (WSOL) methods allow training models to classify images and localize ROIs. WSOL only requires low-cost image-class annotations yet provides a visually interpretable classifier, which is important in histology image analysis. Standard WSOL methods rely on class activation mapping (CAM) methods to produce spatial localization maps according to a single- or two-step strategy. While both strategies have made significant progress, they still face several limitations with histology images. Single-step methods can easily result in under- or over-activation due to the limited visual ROI saliency in histology images and the limited localization cues. They also face the well-known issue of asynchronous convergence between classification and localization tasks. The two-step approach is sub-optimal because it is tied to a frozen classifier, limiting the capacity for localization. Moreover, these methods also struggle when applied to out-of-distribution (OOD) datasets. In this paper, a multi-task approach for WSOL is introduced for simultaneous training of both tasks to address the asynchronous convergence problem. In particular, localization is performed in the pixel-feature space of an image encoder that is shared with classification. This allows learning discriminant features and accurate delineation of foreground/background regions to support ROI localization and image classification. We propose PixelCAM, a cost-effective foreground/background pixel-wise classifier in the pixel-feature space that allows for spatial object localization. PixelCAM is trained using pixel pseudo-labels collected from a pretrained WSOL model. Both image and pixel-wise classifiers are trained simultaneously using standard gradient descent. In addition, our pixel classifier can easily be integrated into CNN- and transformer-based architectures without any modifications.