In environmental sciences, available data are often available at a coarse resolution. This can result in a mismatch between the data resolution and the resolution at which process inferences should be made. This misalignment, usually named as change of support (COS) issue, can lead to biased inferences if not addressed in the models. Yet, solutions to the COS issue have only been proposed for a limited number of simple observational processes (e.g. Poisson or Gaussian processes), which narrows their range of application. Motivated by a fisheries science case study, we introduce a hierarchical method addressing COS issue for zero-inflated data with highly skewed tails. Such data are common in environmental sciences but are not handled by existing COS methods. Our approach requires to know the spatial locations of point-level data and considers that aggregated available data are convolutions of these point-level data. We assess the accuracy of our method through a simulation study, describing different scenarios of COS. Subsequently, we apply our model to a motivating case study, focusing on the distribution of the common sole in the Bay of Biscay. Our findings illustrate that our approach provides better estimates and predictions than the ad hoc methods used to geoprocess aggregated data and refine their resolution.