  We report on the observations of four well-localized binary black hole (BBH)
mergers by the High Energy Stereoscopic System (H.E.S.S.) during the second and
third observing runs of Advanced LIGO and Advanced Virgo, O2 and O3. H.E.S.S.
can observe $\mathrm{20\,deg^2}$ of the sky at a time and follows up
gravitational-wave (GW) events by ``tiling'' localization regions to maximize
the covered localization probability. During O2 and O3, H.E.S.S. observed large
portions of the localization regions, between 35\% and 75\%, for four BBH
mergers (GW170814, GW190512\_180714, GW190728\_064510, and S200224ca). For
these four GW events, we find no significant signal from a pointlike source in
any of the observations, and set upper limits on the very high energy ($>$100
GeV) $\gamma$-ray emission. The 1-10 TeV isotropic luminosity of these GW
events is below $10^{45}$ erg s$^{-1}$ at the times of the H.E.S.S.
observations, around the level of the low-luminosity GRB 190829A. Assuming no
changes are made to how follow-up observations are conducted, H.E.S.S. can
expect to observe over 60 GW events per year in the fourth GW observing run,
O4, of which eight would be observable with minimal latency.
