Sound source localization is a cumbersome task in challenging reverberation conditions. Recently, there is a growing interest in developing learning-based localization methods. In this approach, acoustic features are extracted from the measured signals and then given as input to a model that maps them to the corresponding source positions. Typically, a massive dataset of labeled samples from known positions is required to train such models.Here, we present a novel weakly-supervised deep-learning localization method that exploits only a few labeled (anchor) samples with known positions, together with a larger set of unlabeled samples, for which we only know their relative physical ordering. We design an architecture that uses a stochastic combination of triplet-ranking loss for the unlabeled samples and physical loss for the anchor samples, to learn a nonlinear deep embedding that maps acoustic features to an azimuth angle of the source. The combined loss can be optimized effectively using standard gradient-based approach.Evaluating the proposed approach on simulated data, we demonstrate its significant improvement over two previous learning-based approaches for various reverberation levels, while maintaining consistent performance with varying sizes of labeled data.