  Excitonic states trapped in harmonic moir\'e wells of twisted heterobilayers
is an intriguing testbed. However, the moir\'e potential is primarily governed
by the twist angle, and its dynamic tuning remains a challenge. Here we
demonstrate anharmonic tuning of moir\'e potential in a WS$_2$/WSe$_2$
heterobilayer through gate voltage and optical power. A gate voltage can result
in a local in-plane perturbing field with odd parity around the high-symmetry
points. This allows us to simultaneously observe the first (linear) and second
(parabolic) order Stark shift for the ground state and first excited state,
respectively, of the moir\'e trapped exciton - an effect opposite to
conventional quantum-confined Stark shift. Depending on the degree of
confinement, these excitons exhibit up to twenty-fold gate-tunability in the
lifetime ($100$ to $5$ ns). Also, exciton localization dependent dipolar
repulsion leads to an optical power-induced blueshift of $\sim$1 meV/$\mu$W - a
five-fold enhancement over previous reports.
