Objective: Our aim is to determine if data collected with inertial measurement units (IMUs) during steady-state running could be used to estimate ground reaction forces (GRFs) and to derive biomechanical variables (e.g., contact time, impulse, change in velocity) using lightweight machine-learning approaches. In contrast, state-of-the-art estimation using LSTMs suffers from prohibitive inference times on edge devices, requires expensive training and hyperparameter optimization, and results in black box models. Methods: We proposed a novel lightweight solution, SVD Embedding Regression (SER), using linear regression between SVD embeddings of IMU data and GRF data. We also compared lightweight solutions including SER and k-Nearest-Neighbors (KNN) regression with state-of-the-art LSTMs. Results: We performed extensive experiments to evaluate these techniques under multiple scenarios and combinations of IMU signals and quantified estimation errors for predicting GRFs and biomechanical variables. We did this using training data from different athletes, from the same athlete, or both, and we explored the use of acceleration and angular velocity data from sensors at different locations (sacrum and shanks). Conclusion: Our results illustrated that lightweight solutions such as SER and KNN can be similarly accurate or more accurate than LSTMs. The use of personal data reduced estimation errors of all methods, particularly for most biomechanical variables (as compared to GRFs); moreover, this gain was more pronounced in the lightweight methods. Significance: The study of GRFs is used to characterize the mechanical loading experienced by individuals in movements such as running, which is clinically applicable to identify athletes at risk for stress-related injuries.