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The transition metal dipnictides TaAs _2 , TaSb _2 , NbAs _2 and NbSb _2 have recently sparked interest for exhibiting giant magnetoresistance. While the exact nature of the magnetoresistance in these materials is still under active investigation, there are experimental results indicating that it is of the anisotropic negative variety. We study the effect of magnetic fields on the band structure topology of these materials by applying Zeeman splitting. In the absence of a magnetic field, we find that the materials are weak topological insulators, which is in agreement with previous studies. When the magnetic field is applied, we find that type-II Weyl points form. This result is found first from a symmetry argument, and then numerically for a ${\bf{k}}\cdot {\bf{p}}$ model of TaAs _2 and a tight-binding model of NbSb _2 . This effect could be of help in the search for an explanation of the anomalous magnetoresistance in these materials.