Unknown payloads alter robot dynamics and make precise contact execution difficult when foothold margins are small. We present LOAD, a perceptive locomotion framework that combines explicit inertial estimates with implicit dynamics features for narrow-beam traversal. Separate recurrent modules infer torso inertial changes and task-relevant history from proprioception, while a height-map teacher is distilled into a depth-based student. We extensively evaluate LOAD and its variants in simulation and on hardware across beam widths and payload configurations. The results show that implicit dynamics features accelerate training, while explicit inertial estimation further improves traversal success; combining both enables LOAD to approach the performance of a privileged policy supplied with ground-truth inertial parameters. Hardware experiments demonstrate traversal with unilateral payloads of 6 kg on a 10 cm beam and 9 kg on a 15 cm beam, and an evenly distributed 11 kg payload on a 15 cm beam. These results support combining physical estimates and history features for precision locomotion under unknown loads.

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