This paper focuses on so-called weighted variants of nonnnegative matrix factorization (NMF) and more generally nonnnegative tensor factorization (NTF) approximations. We consider multiplicative update (MU) rules to optimize these approximations, and we prove that under certain conditions the results on monotonicity of MU rules for NMF generalize to both the NTF and the weighted NTF (WNTF) cases.