In the practice of program evaluation, choosing the covariates and the functional form of the propensity score is an important choice that the researchers make when estimating treatment eﬀects. This paper proposes a data-driven way of averaging the estimators over the candidate speciﬁcations in order to resolve the issue of speciﬁcation uncertainty in the propensity score weighting estimation of the average treatment eﬀects for treated (ATT). The proposed averaging procedures aim to minimize the estimated mean squared error (MSE) of the ATT estimator in a local asymptotic framework. We formulate model averaging as a statistical decision problem in a limit experiment, and derive an averaging scheme that is Bayes optimal with respect to a given prior for the localization parameters. Analytical comparisons of the Bayes asymptotic MSE show that the averaging estimator outperforms post model selection estimators and the estimators in any of the candidate models. Our Monte Carlo studies conﬁrm these theoretical results and illustrate the size of the MSE gains from averaging. We apply the averaging procedure to evaluate the eﬀect of the labor market program analyzed in LaLonde (1986).