Molecular weight of nanoparticles is an incorrect term. Nanoparticles are aggregation of individual atoms or molecules. So you are looking for average wight of these aggregates. There are many reports on measuring the weight using mass spectrometry. Please see Chem Commun 2005 Oct 28;(40):5059-61, Anal Chem. 2012 Jun 19;84(12):5304-8, Nature 501, 399–402