Deep Learning (DL) can predict biomarkers directly from digitized cancer histology in a weakly-supervised setting. Recently, the prediction of continuous biomarkers through regression-based DL has seen an increasing interest. Nonetheless, clinical decision making often requires a categorical outcome. Consequently, we developed a weakly-supervised joint multi-task Transformer architecture which has been trained and evaluated on four public patient cohorts for the prediction of two key predictive biomarkers, microsatellite instability (MSI) and homologous recombination deficiency (HRD), trained with auxiliary regression tasks related to the tumor microenvironment. Moreover, we perform a comprehensive benchmark of 16 task balancing approaches for weakly-supervised joint multi-task learning in computational pathology. Using our novel approach, we outperform the state of the art by +7.7% and +4.1% as measured by the area under the receiver operating characteristic, and enhance clustering of latent embeddings by +8% and +5%, for the prediction of MSI and HRD in external cohorts, respectively.