  The proposed topological Kondo insulator SmB$_{6}$ hosts a bulk Kondo
hybridization gap that stems from strong electronic correlations and a metallic
surface state whose effective mass remains disputed. Thermopower and scanning
tunneling spectroscopy measurements argue for heavy surface states that also
stem from strong correlations, whereas quantum oscillation and angle-resolved
photoemission measurements reveal light effective masses that would be
consistent with a Kondo breakdown scenario at the surface. Here we investigate
the evolution of the surface state via electrical and thermoelectric transport
measurements under hydrostatic pressure, a clean symmetry-preserving tuning
parameter that suppresses the Kondo gap and increases the valence of Sm from
2.6+ towards a 3+ magnetic metallic state. Electrical resistivity measurements
reveal that the surface carrier density increases with increasing pressure,
whereas thermopower measurements show an unchanged Fermi energy under pressure.
As a result, the effective mass of the surface state charge carriers linearly
increases with pressure as the Sm valence approaches 3+. Our results are
consistent with the presence of correlation-driven surface states in SmB$_{6}$
and suggest that the surface Kondo effect persists under pressure to 2 GPa.
