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We consider magnetotransport on a helical edge of a quantum spin Hall insulator, in the presence of bulk midgap states side coupled to the edge. In the presence of a magnetic field, the midgap levels are spin split, and hybridization of these levels with the itinerant edge states leads to backscattering, and the ensuing increase in the resistance. We show that there is a singular cusplike contribution to the positive magnetoresistance stemming from resonant midgap states weakly coupled to the edge. The singular behavior persists for both coherent and incoherent edge transport regimes. We use the developed theory to fit the experimental data for the magnetoresistance for monolayer WTe2 at liquid helium temperatures. The results of the fitting suggest that the cusplike behavior of the resistance in weak magnetic fields observed in experiments on monolayer WTe2 with long edge channels might indeed be explained by hybridization of the helical edge states with spin-split bulk midgap states. In particular, the dependence of the magnetoresistance on the direction of the external magnetic field is well described by the incoherent edge transport theory, at the same time being quite distinct from the one expected for a magnetic-field-induced edge gap.