We study the stellar and wind properties of a sample of Galactic O dwarfs to track the conditions under which weak winds (i.e. mass loss rates lower than ~ 10-8 $M_{\odot}$ yr-1) appear. The sample is composed of low and high luminosity dwarfs including Vz stars and stars known to display qualitatively weak winds. Atmosphere models including non-LTE treatment, spherical expansion and line blanketing are computed with the code CMFGEN (Hillier & Miller 1998, ApJ, 496, 407). Both UV and Hα lines are used to derive wind properties while optical H and He lines give the stellar parameters. We find that the stars of our sample are usually 1 to 4 Myr old. Mass loss rates of all stars are found to be lower than expected from the hydrodynam...