Neighborhood rough sets are an effective model for handling numerical and categorical data entangled with vagueness, imprecision, or uncertainty. However, existing neighborhood rough set models and their feature selection methods treat each sample equally, whereas different types of samples inherently play different roles in constructing neighborhood granules and evaluating the goodness of features. In this study, the sample weight information is first introduced into neighborhood rough sets, and a novel weighted neighborhood rough set model is consequently constructed. Then, considering the lack of sample weight information in practical data, a margin-based weight optimization function is designed, based on which a gradient descent algorithm is provided to adaptively learn sample weights through maximizing sample margins. Finally, an average granule margin measure is put forward for feature selection, and a forward-adding heuristic algorithm is developed to generate an optimal feature subset. The proposed method constructs the weighted neighborhood rough sets using sample weights for the first time and is able to yield compact feature subsets with a large margin. Extensive experiments and statistical analysis on UCI datasets show that the proposed method achieves highly competitive performance in terms of feature reduction rate and classification accuracy when compared with other state-of-the-art methods.