Deep regression trackers are among the fastest tracking algorithms available, and therefore suitable for real-time robotic applications. However, their accuracy is inadequate in many domains due to distribution shift and overfitting. In this paper we overcome such limitations by presenting the first methodology for domain adaption of such a class of trackers. To reduce the labeling effort we propose a weakly-supervised adaptation strategy, in which reinforcement learning is used to express weak supervision as a scalar application-dependent and temporally-delayed feedback. At the same time, knowledge distillation is employed to guarantee learning stability and to compress and transfer knowledge from more powerful but slower trackers. Extensive experiments on five different robotic vision domains demonstrate the relevance of our methodology. Real-time speed is achieved on embedded devices and on machines without GPUs, while accuracy reaches significant results.