Traditional geographically weighted regression and its extensions are important methods in the analysis of spatial heterogeneity. However, they are based on distance metrics and kernel functions compressing differences in multidimensional coordinates into one-dimensional values, which rarely consider anisotropy and employ inconsistent definitions of distance in spatio-temporal data or spatial line data (for example). This article proposes a general framework for locally weighted spatial modelling to overcome the drawbacks of existing models using geographically weighted schemes. Underpinning it is a multi-dimensional weighting scheme based on density regression that can be applied to data in any space and is not limited to geographic distance.