Most uses of Meta-Learning in visual recognition are very often applied to image classification, with a relative lack of work in other tasks such as segmentation and detection. We propose a new generic Meta-Learning framework for few-shot weakly supervised segmentation in medical imaging domains. The proposed approach includes a meta-training phase that uses a meta-dataset. It is deployed on an out-of-distribution few-shot target task, where a single highly generalizable model, trained via a selective supervised loss function, is used as a predictor. The model can be trained in several distinct ways, such as second-order optimization, metric learning, and late fusion. Some relevant improvements of existing methods that are part of the proposed approach are presented. We conduct a comparative analysis of meta-learners from distinct paradigms adapted to few-shot image segmentation in different sparsely annotated radiological tasks. The imaging modalities include 2D chest, mammographic, and dental X-rays, as well as 2D slices of volumetric tomography and resonance images. Our experiments consider in total 9 meta-learners, 4 backbones, and multiple target organ segmentation tasks. We explore small-data scenarios in radiology with varying weak annotation styles and densities. Our analysis shows that metric-based meta-learning approaches achieve better segmentation results in tasks with smaller domain shifts compared to the meta-training datasets, while some gradient- and fusion-based meta-learners are more generalizable to larger domain shifts. Guidelines learned from the comparative performance assessment of the analyzed methods are summarized to support those readers interested in the field.