Weakly supervised learning has emerged as a compelling tool for object detection by reducing the need for strong supervision during training. However, major challenges remain: (1) differentiation of object instances can be ambiguous; (2) detectors tend to focus on discriminative parts rather than entire objects; (3) without ground truth, object proposals have to be redundant for high recalls, causing significant memory consumption. Addressing these challenges is difficult, as it often requires to eliminate uncertainties and trivial solutions. To target these issues we develop an instance-aware and context-focused unified framework. It employs an instance-aware self-training algorithm and a learnable Concrete DropBlock while devising a memory-efficient sequential batch back-propagation. Our proposed method achieves state-of-the-art results on COCO (12.1% AP, 24.8% AP50), VOC 2007 (54.9% AP), and VOC 2012 (52.1% AP), improving baselines by great margins. In addition, the proposed method is the first to benchmark ResNet based models and weakly supervised video object detection..