  The existence of $10^9\ {\rm M_\odot}$ supermassive black holes (SMBHs)
within the first billion years of the universe remains a puzzle in our
conventional understanding of black hole formation and growth. Several
suggested formation pathways for these SMBHs lead to a heavy seed, with an
initial black hole mass of $10^4-10^6~{\rm M_\odot}$. This can lead to an
overly massive BH galaxy (OMBG), whose nuclear black hole's mass is comparable
to or even greater than the surrounding stellar mass: the black hole to stellar
mass ratio is $M_{\rm bh}/M_* \gg 10^{-3}$, well in excess of the typical
values at lower redshift. We investigate how long these newborn BHs remain
outliers in the $M_{\rm bh}-M_{*}$ relation, by exploring the subsequent
evolution of two OMBGs previously identified in the \texttt{Renaissance}
simulations. We find that both OMBGs have $M_{\rm bh}/M_* > 1$ during their
entire life, from their birth at $z\approx 15$ until they merge with much more
massive haloes at $z\approx 8$. We find that the OMBGs are spatially resolvable
from their more massive, $10^{11}~{\rm M_\odot}$, neighboring haloes until
their mergers are complete at $z\approx 8$. This affords a window for future
observations with {\it JWST} and sensitive X-ray telescopes to diagnose the
heavy-seed scenario, by detecting similar OMBGs and establishing their uniquely
high black hole-to-stellar mass ratio.
