Weakly supervised machine reading comprehension (MRC) task is practical and promising for its easily available and massive training data, but inevitablely introduces noise. Existing related methods usually incorporate extra submodels to help filter noise before the noisy data is input to main models. However, these multistage methods often make training difficult, and the qualities of submodels are hard to be controlled. In this paper, we first explore and analyze the essential characteristics of noise from the perspective of loss distribution, and find that in the early stage of training, noisy samples usually lead to significantly larger loss values than clean ones. Based on the observation, we propose a hierarchical loss correction strategy to avoid fitting noise and enhance clean supervision signals, including using an unsupervisedly fitted Gaussian mixture model to calculate the weight factors for all losses to correct the loss distribution, and employ a hard bootstrapping loss to modify loss function. Experimental results on different weakly supervised MRC datasets show that the proposed methods can help improve models significantly.