Since the preparation of labeled data for training semantic segmentation networks of point clouds is a time-consuming process, weakly supervised approaches have been introduced to learn from only a small fraction of data. These methods are typically based on learning with contrastive losses while automatically deriving per-point pseudo-labels from a sparse set of user-annotated labels. In this paper, our key observation is that the selection of which samples to annotate is as important as how these samples are used for training. Thus, we introduce a method for weakly supervised segmentation of 3D scenes that combines self-training with active learning. Active learning selects points for annotation that are likely to result in improvements to the trained model, while self-training makes efficient use of the user-provided labels for learning the model. We demonstrate that our approach leads to an effective method that provides improvements in scene segmentation over previous work and baselines, while requiring only a few user annotations.