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Geographically Weighted Regression (GWR) has gained widespread popularity across various disciplines for investigating spatial heterogeneity with respect to data relationships in georeferenced datasets. However, GWR is typically limited to the analysis of continuous dependent variables, which are assumed to follow a symmetric normal distribution. In many fields, nonnegative continuous data are often observed and may contain substantial amounts of zeros followed by a right-skewed distribution of positive values. When dealing with such type of outcomes, GWR may not provide adequate insights into spatially varying regression relationships. This study intends to extend the GWR based on a compound Poisson distribution. Such an extension not only allows for exploration of relationship heterogeneity but also accommodates nonnegative continuous response variables. We provide a detailed specification of the proposed model and discuss related modeling issues. Through simulation experiments, we assess the performance of this novel approach. Finally, we present an empirical case study using a dataset on dengue fever in Tainan, Taiwan, to demonstrate the practical applicability and utility of our proposed methodology.