  In the upcoming gravitational wave (GW) observing runs, identifying host
galaxies is crucial as it provides essential redshift information and enables
the use of GW events as standard sirens. However, pinpointing host galaxies
remains challenging due to the large localization uncertainties and the rapidly
fading nature of their optical counterparts. Analyzing the host galaxies of
short gamma-ray bursts (sGRBs) offers an alternative approach to deepen our
understanding of the environments where binary neutron stars (BNS) primarily
merge. This study compiles archival photometric data for the host galaxies of
76 sGRBs and 4 hybrid GRBs that are long GRBs accompanied by kilonova-like
signals. We use this data to evaluate their physical properties through
spectral energy distribution (SED) fitting. To assess the characteristics of
the host galaxies, we utilized a volume-limited sample ($z<0.5$) from the
COSMOS field as a control group. Contrary to expectations that the BNS merger
rate is proportional to host stellar mass, the short and hybrid GRB population
appears less massive than the mass-weighted distribution of the control sample.
Instead, we propose a formulation for the expected BNS merger rate from a
galaxy as $\log(n_{\mathrm{BNS}}/\mathrm{Gyr}) = 0.86 \times
\log(M_*/M_{\odot}) + 0.44 \times \log(\mathrm{sSFR}/\mathrm{yr}) + 0.857$,
which optimally explains the deviation between the stellar mass distributions
of the GRB host galaxies and the control sample. These insights provide a
strategic framework for targeted GW follow-ups and enhance our ability to
identify potential host galaxies for future GW events.
