We evaluate the effectiveness of importance weighting in deep neural networks under label shift and covariate shift. On synthetic 2D data (linearly separable and moon-shaped) using logistic regression and MLPs, we observe that weighting strongly affects decision boundaries early in training but fades with prolonged optimization. On CIFAR-10 with various class imbalances, only L2 regularization (not dropout) helps preserve weighting effects. In a covariate-shift experiment, importance weighting yields no significant performance gain, highlighting challenges on complex data. Our results call into question the practical utility of importance weighting for real-world distribution shifts.