Analyses of Galactic late O dwarfs (O8-O9.5V) raised the `weak wind problem: spectroscopic mass loss rates ($dot{M}$) are up to two orders of magnitude lower than the theoretical values. We investigated the stellar and wind properties of Galactic late O giants (O8-O9.5III). We performed a spectroscopic analysis of nine O8-O9.5III stars in the ultraviolet (UV) and optical regions using the model atmosphere code CMFGEN. From the UV region, we found $dot{M}$ $sim$ $10^{-8}-10^{-9}$ $mathrm{M_odot}$ $mathrm{yr^{-1}}$ overall. This is lower by $sim 0.9 - 2.3$ dex than the predicted values based on the (global) conservation of energy in the wind. The mass-loss rates predicted from first principles, based on the moving reversing layer theory, agree better with our findings, but it fails to match the spectroscopic $dot{M}$ for the most luminous OB stars. The region of $log(L_star/L_odot) sim 5.2$ is critical for both sets of predictions in comparison with the spectroscopic mass-loss rates. CMFGEN models with the predicted $dot{M}$ (the former one) fail to reproduce the UV wind lines for all the stars of our sample. We reproduce the observed H$alpha$ profiles of four objects with our $dot{M}$ derived from the UV. Hence, low $dot{M}$ values (weak winds) are favored to fit the observations (UV + optical), but discrepancies between the UV and H$alpha$ diagnostics remain for some objects. Our results indicate weak winds beyond the O8-9.5V class, since the region of $log(L_star/L_odot) sim 5.2$ is indeed critical to the weak wind phenomenon. Since O8-O9.5III stars are more evolved than O8-9.5V, evolutionary effects do not seem to play a role in the onset of the weak wind phenomenon. These findings support that the $dot{M}$ (for low luminosity O stars) in use in the majority of modern stellar evolution codes must be severely overestimated up to the end of the H-burning phase.
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