The scaling of nuclear-spin-dependent parity-violating effects with increasing nuclear charge Z is discussed in two series of isoelectronic open-shell diatomic molecules. The parameter W_a characterizing the strength of parity violation in diatomic molecules is calculated in the framework of the zeroth-order regular approximation and found to be in good agreement with the R(Z)Zk scaling law derived for atoms, in which R(Z) represents a relativistic enhancement factor. The influence of electron correlation is studied on the molecular level, with spin-polarization effects being conveniently accounted for by a previously established approximate relation between the hyperfine coupling tensor and W_a. For high-accuracy predictions of parity-violating effects in radium fluoride, the necessity for systematically improvable correlation calculations is emphasized.