Unconfounded comparisons of multiple groups are common in observational studies. Motivated from a racial disparity study in health services research, we propose a unified framework, the balancing weights, for estimating causal effects with multiple treatments using propensity score weighting. The class of balancing weights include existing approaches such as inverse probability weights as special cases. Within this framework, we propose a class of target estimands and their corresponding nonparametric weighting estimators. We further develop the generalized overlap weights, constructed as the product of the inverse probability weights and the harmonic mean of the generalized propensity scores. The generalized overlap weights correspond to the target population with the most overlap in covariates between treatments, similar to the population in equipoise in clinical trials. We show that the generalized overlap weights minimize the total asymptotic variance of the weighting estimators for the pairwise contrasts within the class of balancing weights. We apply these methods to study the racial disparities in medical expenditure and further examine their properties by simulations.