  The most massive stars are thought to be hydrogen-rich Wolf-Rayet stars of
late spectral subtype (WNh stars). In previous theoretical studies the enhanced
mass loss of these stars has been attributed to their proximity to the
Eddington limit. Here we investigate observed trends in the mass-loss
properties of such young, very massive stars. We derive theoretical
mass-luminosity relations for very massive stars, based on a large grid of
stellar structure models. Using these relations, we estimate Eddington factors
for a sample of stars, under different assumptions of their evolutionary
status. We evaluate the resulting mass-loss relations, and compare them with
theoretical predictions. We find observational evidence that the mass loss in
the WR regime is dominated by the Eddington parameter Gamma_e, which has
important consequences for the way we understand Wolf-Rayet stars and their
mass loss. In addition, we derive wind masses that support the picture that the
WNh stars in young stellar clusters are very massive, hydrogen-burning stars.
Our findings suggest that the proximity to the Eddington limit is the physical
reason for the onset of Wolf-Rayet type mass loss. This means that, e.g. in
stellar evolution models, the Wolf-Rayet stage should be identified by large
Eddington parameters, instead of a helium-enriched surface composition. The
latter is most likely only a consequence of strong mass loss, in combination
with internal mixing. For very massive stars, the enhanced Gamma-dependent mass
loss is responsible for the formation of late WNh subtypes with high hydrogen
surface abundances, partly close to solar. Because mass loss dominates the
evolution of very massive stars, we expect a strong impact of this effect on
their end products, in particular on the potential formation of black holes,
and Gamma-Ray Bursts, as well as the observed upper mass limit of stars.
