External research funding is an essential component of the infrastructure of modern, academic research. Priorities in funding decisions drive what knowledge is generated, and how scientists' careers are shaped. For health research, it can ultimately have implications for health outcomes. The aim of this paper is to illustrate how funding information can be used to track priorities in health research, linking them to disease burdens and research outputs. Furthermore, funding concentrations are analysed from both researcher and disease perspectives, to estimate the influence of personal Matthew-effects on the distribution of health research funding. Denmark is used as the case, including funding information from all major public and private research foundations in the period 2004-2016. Grant information is linked to research outputs and disability-adjusted life-years (DALY rates), for 34,160 publications linked to 2630 grants, receiving DKK 4.8 billion in funding. Data show poor correlation between funding priorities, research activity and disease burdens, with several diseases receiving disproportionate amounts of funding. A research opportunity index is calculated to identify diseases with the highest potential for future investments from a burden-centred point of view. Funding is highly concentrated, both on people and on specific diseases. High funding concentrations on researchers can be a driving factor behind the observed funding-to-burden imbalances, and may risk knowledge stagnation through monopolisation of the market place of ideas. Results indicate that funders of clinical and translational research, as well as some types of biomedical research, need to supplement traditional considerations of scientific excellence with measures of societal challenges and relevance.