The connections among galaxies, the dark matter haloes where they form and the properties of the large-scale Cosmic Web still need to be completely disentangled. We use the cosmological hydrodynamical simulation TNG100 of the IllustrisTNG suite to quantify the effects played by the large-scale density field and the Cosmic Web morphology on the relation between halo mass and galaxy stellar mass. We select objects with total dynamical mass in the range >= 6.3 x 10(10) h(-1)M(circle dot) up to a few 10(14) h(-1)M(circle dot) between redshift z = 4 and redshift z = 0. A Cosmic Web class (knot, filament, sheet, void) is assigned to each region of the volume using a density field deformation tensor-based method. We find that galaxy stellar mass strongly correlates with total dynamical mass and formation time, and more weakly with large-scale overdensity and Cosmic Web class. The latter two quantities correlate with each other, but are not entirely degenerate. Furthermore, we find that at fixed halo mass, galaxies with stellar mass lower than the median value are more likely to be found in voids and sheets, whereas galaxies with stellar mass higher than the median are more likely to be found in filaments and knots. Finally, we find that the dependence on environment is stronger for satellites than for centrals, and discuss the physical implications of these results.