Federated Learning supports collaborative model training across distributed clients while keeping sensitive data decentralized. Still, non-independent and identically distributed data pose challenges like unstable convergence and client drift. We propose Federated Normalized Loss-based Weighted Aggregation (FedNolowe), a new method that weights client contributions using normalized training losses, favoring those with lower losses to improve global model stability. Unlike prior methods tied to dataset sizes or resource-heavy techniques, FedNolowe employs a two-stage Manhattan normalization, reducing computational complexity by 40% in floating-point operations while matching state-of-the-art performance. A detailed sensitivity analysis shows our two-stage weighting maintains stability in heterogeneous settings by mitigating extreme loss impacts while remaining effective in independent and identically distributed scenarios.