The onset of the COVID-19 pandemic accentuated the need for access to biomedical literature to answer timely and disease-specific questions. During the early days of the pandemic, one of the biggest challenges we faced was the lack of peer-reviewed biomedical articles on COVID-19 that could be used to train machine learning models for question answering (QA). In this paper, we explore the roles weak supervision and data augmentation play in training deep neural network QA models. First, we investigate whether labels generated automatically from the structured abstracts of scholarly papers using an information retrieval algorithm, BM25, provide a weak supervision signal to train an extractive QA model. We also curate new QA pairs using information retrieval techniques, guided by the clinicaltrials.gov schema and the structured abstracts of articles, in the absence of annotated data from biomedical domain experts. Furthermore, we explore augmenting the training data of a deep neural network model with linguistic features from external sources such as lexical databases to account for variations in word morphology and meaning. To better utilize our training data, we apply curriculum learning to domain adaptation, fine-tuning our QA model in stages based on characteristics of the QA pairs. We evaluate our methods in the context of QA models at the core of a system to answer questions about COVID-19.