Despite the extensive usage of point clouds in 3D vision, relatively limited data are available for training deep neural networks. Although data augmentation is a standard approach to compensate for the scarcity of data, it has been less explored in the point cloud literature. In this paper, we propose a simple and effective augmentation method called PointWOLF for point cloud augmentation. The proposed method produces smoothly varying non-rigid deformations by locally weighted transformations centered at multiple anchor points. The smooth deformations allow diverse and realistic augmentations. Furthermore, in order to minimize the manual efforts to search the optimal hyperparameters for augmentation, we present AugTune, which generates augmented samples of desired difficulties producing targeted confidence scores. Our experiments show our framework consistently improves the performance for both shape classification and part segmentation tasks. Particularly, with PointNet++, PointWOLF achieves the state-of-the-art 89.7 accuracy on shape classification with the real-world ScanObjectNN dataset. The code is available at https://github.com/mlvlab/PointWOLF.