Nuclear spin-dependent parity violation effects are predicted with the help of a quasi-relativistic two-component zeroth order regular approximation (ZORA) approach for a series of open-shell diatomic molecules that feature a ²Σ electronic ground state. The particular focus is on scaling behaviour of the parity violating parameter W_a in the effective spin-rotational Hamiltonion with increasing nuclear charge Z of the heavier atom in the diatomic molecule. Previously (Isaev and Berger, 2012) an approximate R(A,Z) Z² scaling law, with R(A,Z) denoting a relativistic enhancement factor, was confirmed for W_a in the series of valence isoelectronic group II monofluorides and valence isoelectronic group XII monohydrides, that is along columns of the periodic table of the elements. In this work, a pronounced R(A,Z) Z^k scaling is predicted for isolobal ²Σ diatomic molecules along rows of the periodic table, with k being approximately 4 and 6 for the fourth and fifth row, respectively, and even larger for the sixth and seventh row. This observation opens up a another dimension in the systematic search of candidate systems for measuring nuclear spin-dependent parity violating interactions in molecules.