Aims. Analyses of Galactic late O dwarfs (O8-O9.5V stars) raised the "weak wind problem": spectroscopic mass-loss rates (Ṁ) 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 stars). These stars have luminosities log(L /L ) ∼ 5.2, which is the critical value (onset of weak winds) proposed in the literature. Methods. We performed a spectroscopic analysis of nine O8-O9.5III stars in the ultraviolet (UV) and optical regions using the model atmosphere code CMFGEN. Results. Stellar luminosities were adopted using calibrations from the literature. Overall, our model spectral energy distributions agree well with the observed ones considering parallaxes from the latest GAIA data release (DR2). The effective temperature derived from the UV region agrees well with the ones from the optical. As expected, the analysis of the Hertzsprung-Russell (HR) diagram shows that our sample is more evolved than late O dwarfs. From the UV region, we foundṀ ∼ 10 −8 − 10 −9 M yr -1 overall. This is lower by ∼ 0.9 − 2.3 dex than 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 spectroscopiċ M for the most luminous OB stars. The region of log(L /L ) ∼ 5.2 is critical for both sets of predictions in comparison with the spectroscopic mass-loss rates. CMFGEN models with the predictedṀ (the former one) fail to reproduce the UV wind lines for all the stars of our sample. We reproduce the observed Hα profiles of four objects with ourṀ derived from the UV. Hence, lowṀ values (weak winds) are favored to fit the observations (UV + optical), but discrepancies between the UV and Hα diagnostics remain for some objects. Conclusions. Our results indicate weak winds beyond the O8-9.5V class, since the region of log(L /L ) ∼ 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 theṀ (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. Further investigations must evaluate the consequences of weak winds in terms of physical parameters for massive stars (e.g., angular momentum and CNO surface abundances).