  We investigate the interplay between numerical relativity (NR) and
point-particle black hole perturbation theory (ppBHPT) in the comparable mass
ratio regime. In the ppBHPT framework, the secondary black hole is treated as a
point particle, neglecting its finite size. Our study focuses on addressing the
missing finite size effect in the ppBHPT framework and proposing a method for
incorporating the size of the secondary into the perturbation theory framework.
We demonstrate that by considering the secondary as a finite size object, the
BHPT waveforms closely match NR waveforms. Additionally, we revisit the
$\alpha$-$\beta$ scaling technique, which was previously introduced by Islam et
al, as a means to effectively match ppBHPT waveforms to NR waveforms. We
further analyze the scaling procedure and decompose it into different
components, attributing them to various effects, including the corrections
arising from the finite size of the secondary black hole.
