  The spins of merging binary black holes offer insights into their formation
history. Recently it has been argued that in isolated binary evolution of two
massive stars the firstborn black hole is slowly rotating, whilst the
progenitor of the second-born black hole can be tidally spun up if the binary
is tight enough. Naively, one might therefore expect that only the less massive
black hole in merging binaries exhibits non-negligible spin. However, if the
mass ratio of the binary is "reversed" (typically during the first mass
transfer episode), it is possible for the tidally spun up second-born to become
the more massive black hole. We study the properties of such mass-ratio
reversed (MRR) binary black hole mergers using a large set of 560 population
synthesis models. We find that the more massive black hole is formed second in
$\gtrsim 70\%$ of binary black holes observable by LIGO, Virgo, and KAGRA for
most model variations we consider, with typical total masses $\gtrsim 20$
M$_{\odot}$ and mass ratios $q = m_2 / m_1 \sim 0.7$ (where $m_1 > m_2$). The
formation history of these systems typically involves only stable mass transfer
episodes. The second-born black hole has non-negligible spin ($\chi > 0.05$) in
up to $25\%$ of binary black holes, with among those the more (less) massive
black hole spinning in $0\%$--$80\%$ ($20\%$--$100\%$) of cases, varying
greatly in our models. We discuss our models in the context of several observed
gravitational-wave events and the observed mass ratio - effective spin
correlation.
