  Gravitational waves from merging binary black holes can be used to shed light
on poorly understood aspects of massive binary stellar evolution, such as the
evolution of massive stars (including their mass-loss rates), the common
envelope phase, and the rate at which massive stars form throughout the cosmic
history of the Universe. In this paper we explore the \emph{correlated} impact
of these phases on predictions for the merger rate and chirp mass distribution
of merging binary black holes, aiming to identify possible degeneracies between
model parameters. In many of our models, a large fraction (more than 70% of
detectable binary black holes) arise from the chemically homogeneous evolution
scenario; these models tend to over-predict the binary black hole merger rate
and produce systems which are on average too massive. Our preferred models
favour enhanced mass-loss rates for helium rich Wolf--Rayet stars, in tension
with recent theoretical and observational developments. We identify
correlations between the impact of the mass-loss rates of Wolf--Rayet stars and
the metallicity evolution of the Universe on the rates and properties of
merging binary black holes. Based on the observed mass distribution, we argue
that the $\sim 10\%$ of binary black holes with chirp masses greater than $40$
M$_\odot$ (the maximum predicted by our models) are unlikely to have formed
through isolated binary evolution, implying a significant contribution (> 10%)
from other formation channels such as dense star clusters or active galactic
nuclei. Our models will enable inference on the uncertain parameters governing
binary evolution in the near future.
