The propensity score is widely used for causal inference in observational studies, but common parametric estimators can produce biased and inefficient effect estimates when model assumptions are violated. Nonparametric approaches reduce sensitivity to misspecification but often yield unstable weights and inadequate covariate balance. We propose Local Balance with Calibration, implemented by Neural Networks, a weighting method that combines flexible function approximation with the explicit enforcement of covariate balance and calibration. When used with inverse probability weighting, the proposed estimator produces more stable weights, improved covariate balance, and reduced bias in average treatment effect estimation compared with existing approaches. We further develop an influence-function-based variance estimator that provides accurate uncertainty quantification for the resulting weighted estimators. Numerical studies demonstrate improved efficiency and reliable variance estimation across a range of data-generating scenarios. The method is implemented using the publicly available R package LBCNet.

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