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 approaches of task balancing for weakly-supervised joint multi-task learning in computational pathology. Using our novel approach, we improve over the state-of-the-art area under the receiver operating characteristic by +7.7% and +4.1%, as well as yielding better clustering of latent embeddings by +8% and +5% for the prediction of MSI and HRD in external cohorts, respectively.