Bayesian hierarchical regression (BHR) is often used in small area estimation (SAE). BHR conditions on the samples. Therefore, when data are from a complex sample survey, neither survey sampling design nor survey weights are used. This can introduce bias and/or cause large variance. Further, if non-informative priors are used, BHR often requires the combination of multiple years of data to produce sample sizes that yield adequate precision; this can result in poor timeliness and can obscure trends. To address bias and variance, we propose a design assisted model-based approach for SAE by integrating adjusted sample weights. To address timeliness, we use historical data to define informative priors (power prior); this allows estimates to be derived from a single year of data. Using American Community Survey data for validation, we applied the proposed method to Behavioral Risk Factor Surveillance System data. We estimated the prevalence of disability for all U.S. counties. We show that our method can produce estimates that are both more timely than those arising from widely-used alternatives and are closer to ACS’ direct estimates, particularly for low-data counties. Our method can be generalized to estimate the county-level prevalence of other health related measurements.