Batch Normalization (BN) is widely adopted to enable faster convergence and more stable training of deep neural networks. However, its impact on privacy and memorization has remained largely unexplored. In this work, we investigate the effect of BN layers on the memorization of atypical or outlier samples and its implications for privacy leakage. We conduct an extensive empirical study using three complementary approaches: (i) unintended memorization of out-of-distribution training samples, (ii) per-sample influence measured via gradient norms, and (iii) susceptibility to membership inference attacks (MIA). Across multiple datasets and architectures, we consistently observe that BN substantially increases the memorization of outliers compared to models without BN. Critically, this amplified memorization translates directly into privacy vulnerabilities: models with BN exhibit significantly higher susceptibility to MIAs. We complement our empirical findings with a theoretical analysis showing that BN amplifies the per-step influence of outlier samples during training, providing mechanistic insight into this phenomenon. Our results highlight an underappreciated privacy risk associated with BN and provide both practical and theoretical insights into how normalization layers can amplify the influence of rare or sensitive training examples.