Despite their success, deep networks have been shown to be highly susceptible to perturbations, often causing significant drops in accuracy. In this paper, we investigate model robustness on perturbed inputs by studying the performance of internal sub-networks (subnets). Interestingly, we observe that most subnets show particularly poor robustness against perturbations. More importantly, these weak subnets are correlated with the overall lack of robustness. Tackling this phenomenon, we propose a new training procedure that identifies and enhances weak subnets (EWS) to improve robustness. Specifically, we develop a search algorithm to find particularly weak subnets and explicitly strengthen them via knowledge distillation from the full network. We show that EWS greatly improves both robustness against corrupted images as well as accuracy on clean data. Being complementary to popular data augmentation methods, EWS consistently improves robustness when combined with these approaches. To highlight the flexibility of our approach, we combine EWS also with popular adversarial training methods resulting in improved adversarial robustness.