Microstructure-weighted connectomes incorporate diffusion parameters into structural networks, offering a rich characterisation of brain connectivity. While these biologically-informed connectomes have shown sensitivity to pathology-related alterations (for example in multiple sclerosis), their reproducibility remains largely unexplored. In this study, we evaluated the consistency of connectomes weighted with tensor and Bingham-NODDI parameters, employing a four-shell acquisition protocol to ensure accurate fibre reconstruction. Phantom and in vivo (N=4) data were acquired to assess temporal, inter-site and inter-protocol reproducibility of weighting parameters and inter-site stability of graph metrics. High reproducibility was observed for fractional anisotropy (FA), mean diffusivity (MD), and intra-neurite (INVF) and intra-cellular (ICVF) volume fractions, with coefficients of variation (CVs) below 5% and negligible Bland-Altman biases. Orientation dispersion index and β concentration parameter showed CVs above 5% and were excluded from connectome construction. Graph metrics extracted from FA-, MD- and INVF-weighted connectomes exhibited good consistency, except for modularity. Extra-cellular volume fraction (ECVF)-weighted connectomes showed poor reproducibility (CV>5%, intraclass correlation coefficient <0.5). These preliminary findings demonstrate the reliability of microstructure-weighted connectomes, identifying the weighting strategies and graph metrics with the highest reproducibility. This supports the use of network metrics derived from weighted connectomes as potential biomarkers of altered brain connectivity in neurological disorders.