Affect preferences vary with user demographics, and tapping into demographic information provides important cues about the users' language preferences. In this paper, we utilize the user demographics and propose EmpathBERT, a demographic-aware framework for empathy prediction based on BERT. Through several comparative experiments, we show that EmpathBERT surpasses traditional machine learning and deep learning models, and illustrate the importance of user demographics, for predicting empathy and distress in user responses to stimulative news articles. We also highlight the importance of affect information in the responses by developing affect-aware models to predict user demographic attributes.