Weighted linear combination is a multi-criteria decision analysis technique that can be used by decision-makers to select an optimal location from a collection of alternative locations. Its local form takes into account the range of attribute values within a user-defined neighbourhood in accordance with the range-sensitivity principle. This research explores locally weighted linear combination in a vector-based geographic information system. A custom application in ArcGIS 10 allows the user to select a neighbourhood definition from a standard set including contiguity, distance, and k-nearest neighbours, for which local weights are generated. A case study on vulnerability to heat-related illness in Toronto is used to illustrate the technique. The impact of local weighting on the heat vulnerability index is examined using visual analysis of the spatial patterns of heat vulnerability under the global and local approaches, as well as the sensitivity of the local approach to the selected neighbourhood definition. A trade-off analysis of the local weights is also presented. The combination of socio-demographic and environmental determinants in a locally weighted index results in patterns of heat vulnerability that could support targeted hot weather response at a micro-geographic level within urban neighbourhoods.