We investigate the problem of classifying - from a single image the level of content in a cup or a drinking glass. This problem is made challenging by several ambiguities caused by transparencies, shape variations and partial occlusions, and by the availability of only small training datasets. In this paper, we tackle this problem with an appropriate strategy for transfer learning. Specifically, we use adversarial training in a generic source dataset and then refine the training with a task-specific dataset. We also discuss and experimentally evaluate several training strategies and their combination on a range of container types of the CORSMAL Containers Manipulation dataset. We show that transfer learning with adversarial training in the source domain consistently improves the classification accuracy on the test set and limits the overfitting of the classifier to specific features of the training data.