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Real phenomena often leads to challenges in data. One of these is outliers or influential values. Especially in a small sample, these values can have a major influence on the modeling process. In the beta regression framework, this issue has been addressed mainly in two ways: the assumption of a different response model and the application of a minimum density power divergence estimation (MDPDE) procedure. In this paper, however, we propose a simple hierarchical Bayesian methodology in the context of a varying dispersion beta response model that is robust to outliers, as shown through an extensive simulation study and analysis of two real data sets. To robustify Bayesian modeling, a heavy-tailed Student's t prior with uniform degrees of freedom is adopted for the regression coefficients. This proposal results in a wieldy implementation procedure which avails practical use of the approach. [ABSTRACT FROM AUTHOR]