The paper problematises the reliability and ethics of using social media data, such as sourced from Twitter or Instagram, to carry out health-related research. As in many other domains, the opportunity to mine social media for information has been hailed as transformative for research on well-being and disease. Considerations around the fairness, responsibilities and accountabilities relating to using such data have often been set aside, on the understanding that as long as data were anonymised, no real ethical or scientific issue (...) would arise. We first counter this perception by emphasising that the use of social media data in health research can yield problematic and unethical results. We then provide a conceptualisation of methodological data fairness that can complement data management principles such as FAIR by enhancing the actionability of social media data for future research. We highlight the forms that methodological data fairness can take at different stages of the research process and identify practical steps through which researchers can ensure that their practices and outcomes are scientifically sound as well as fair to society at large. We conclude that making research data fair as well as FAIR is inextricably linked to concerns around the adequacy of data practices. The failure to act on those concerns raises serious ethical, methodological and epistemic issues with the knowledge and evidence that are being produced. (shrink)