We consider an emerging user-guided audio source separation approach based on the temporal annotation of the source activity along the mixture. In this baseline algorithm nonnegative matrix factorization (NMF) is usually used as spectral model for audio sources. In this paper we propose two weighting strategies incorporated in the NMF formulation so as to better exploit the annotation. We then derive the corresponding multiplicative update (MU) rules for the parameter estimation. The proposed approach was objectively evaluated within the fourth community-based Signal Separation Evaluation Campaign (SiSEC 2013) and shown to outperform the baseline algorithm, while obtaining comparable result to some other state-of-the-art methods.