Contactless Human Activity Recognition (HAR) has played a critical role in smart healthcare and elderly care homes to monitor patient behavior and detect falls or abnormal activities in real time. The effectiveness of non-invasive HAR is often hindered by location-centric variations in Channel State Information (CSI). These variations limit the ability of HAR models to generalize across new unseen cross-domain environments; for instance, a model trained in one location might not perform well in another physical location. To address this challenge, in this study, we present a novel federated learning (FL) algorithm designed to train a robust global model from local datasets in different localizations. The proposed Federated Weighted Averaging for HAR (Fed-WAHAR) algorithm mitigates location-induced disparities, including heterogeneity and non-Independent and Identically Distributed (non-IID) data distributions. Fed-WAHAR employs a dynamic weighting approach based on local models' accuracy to improve global model classification accuracy and reduce convergence time effectively. We evaluated the performance of Fed-WAHAR using various metrics, including accuracy, precision, recall, F1 score, confusion matrix, and convergence analysis. Experimental results demonstrate that Fed-WAHAR achieves an accuracy of 85% in recognizing human activities across different locations, enhancing the ability of the model to infer across new unseen locations.