Community detection methods have been extensively studied to recover communities structures in network data. While many models and methods focus on binary data, real-world networks also present the strength of connections, which could be considered in the network analysis. We propose a probabilistic model for generating weighted networks that allows us to control network sparsity and incorporates degree corrections for each node. We propose a community detection method based on the Variational Expectation-Maximization (VEM) algorithm. We show that the proposed method works well in practice for simulated networks. We analyze the Brazilian airport network to compare the community structures before and during the COVID-19 pandemic.