Evidence-informed and equity-oriented public health policy and practice require that people’s voices, especially those less heard, be central to decision-making in public health (Serrant-Green 2011). Stakeholder engagement is particularly urgent in the context of health inequities, where perspectives of those who carry the greatest burden of inequities are often poorly reflected in published literature (Serrant-Green 2011). Decision-makers in public health need robust and locally relevant tools that take account of both biomedical and cultural understandings of health and that support people’s participation in planning, implementation and evaluation (Napier et al. 2014). Leveraging several well-established tools from participatory research, systems science and Bayesian analysis, under a critical realist philosophy, we present a novel approach to knowledge synthesis, called the Weight of Evidence. This approach pushes conventional boundaries of who (or what) constitutes health service expertise through the formal inclusion of experiential knowledge from patients and/or communities, care providers and resource decision-makers, together on even footing with epidemiological studies (Borda 1996; Midgley 2000). This method unfolds in five steps: A conventional mixed methods synthesis of the research literature summarizes what is known about an outcome of interest, representing this knowledge as a map; Independently, stakeholders generate cognitive maps that identify and weight factors they believe influence the outcome; Update the literature-based map with stakeholder knowledge using Bayesian analysis; Suggest explanations of how social, economic and organizational contexts contribute to outcomes prioritized in cognitive maps; stakeholders adjust these explanations according to their experience; and Stakeholders develop recommendations accordingly. In this publication, we outline the Weight of Evidence process, highlighting some of the key insights from our pilot work addressing inequities in perinatal health in Canada, while a full description of our methodological development results is forthcoming. Weight of Evidence proved an excellent way to engage meaningfully with divergent perspectives, creating space for multiple and complex ways of understanding health and health services. Mapping evidence Step 1 follows existing guidelines to support comprehensive mixed methods evidence syntheses, pooling effect estimates when appropriate using standard meta-analyses techniques (Pluye and Hong 2014). We converted all effect estimates to odds ratios and transformed them into a common scale (− 1 to + 1) (Andersson et al. 2017). We then summarized findings in a concept map where nodes in the map represent themes from qualitative studies or independent variables from quantitative studies, and the strength of the arcs connecting nodes describe the effect estimates (Ozesmi and Ozesmi 2004; Giles et al. 2008). In our demonstration case, we focused on unmet postpartum care needs among recent immigrant women as an important health inequity in Canada (Gagnon et al. 2013). Our concept map also included evidence from the broader literature on perinatal health outcomes and experiences of recent immigrant women in Canada, as shown in Fig. 1. Open in a separate window Fig. 1 Fuzzy cognitive map of available literature on unmet postpartum care needs among recent immigrant women in Canada. EPDS is the Edinburgh Postnatal Depression Scale. A score greater than 13 on the EPDS is interpreted as probable depression (Cox et al. 1987) (Canada, 2016)