Statistical agencies utilize models to synthesize respondent-level data for release to the general public as an alternative to the actual data records. A Bayesian model synthesizer encodes privacy protection by employing a hierarchical prior construction that induces smoothing of the real data distribution. Synthetic respondent-level data records are often preferred to summary data tables due to the many possible uses by researchers and data analysts. Agencies balance a trade-off between utility of the synthetic data versus disclosure risks and hold a specific target threshold for disclosure risk before releasing synthetic datasets. We introduce a pseudo posterior likelihood that exponentiates each contribution by an observation record-indexed weight in (0, 1), defined to be inversely proportional to the disclosure risk for that record in the synthetic data. Our use of a vector of weights allows more precise downweighting of high risk records in a fashion that better preserves utility as compared with using a scalar weight. We illustrate our method with a simulation study and an application to the Consumer Expenditure Survey of the U.S. Bureau of Labor Statistics. We demonstrate how the frequentist consistency and uncertainty quantification are affected by the inverse risk-weighting.