  We study weak Harnack inequality and a priori H\"older regularity of harmonic
functions for symmetric nonlocal Dirichlet forms on metric measure spaces with
volume doubling condition. Our analysis relies on three main assumptions: the
existence of a strongly local Dirichlet form with sub-Gaussian heat kernel
estimates, a tail estimate of the jump measure outside balls and a local energy
comparability condition. We establish the robustness of our results, ensuring
that the constants in our estimates remain bounded, provided that the order of
the scale function appearing in the tail estimate and local energy
comparability condition, maintains a certain distance from zero. Additionally,
we establish a sufficient condition for the local energy comparability
condition.
