In most settings of practical concern, machine learning practitioners know in advance what end-task they wish to boost with auxiliary tasks. However, widely used methods for leveraging auxiliary data like pre-training and its continued-pretraining variant are end-task agnostic: they rarely, if ever, exploit knowledge of the target task. We study replacing end-task agnostic continued training of pre-trained language models with end-task aware training of said models. We argue that for sufficiently important end-tasks, the benefits of leveraging auxiliary data in a task-aware fashion can justify forgoing the traditional approach of obtaining generic, end-task agnostic representations as with (continued) pre-training. On three different low-resource NLP tasks from two domains, we demonstrate that multi-tasking the end-task and auxiliary objectives results in significantly better downstream task performance than the widely-used task-agnostic continued pre-training paradigm of Gururangan et al. (2020).We next introduce an online meta-learning algorithm that learns a set of multi-task weights to better balance among our multiple auxiliary objectives, achieving further improvements on end-task performance and data efficiency.