  In the presence of a large perpendicular electric field, Bernal-stacked
bilayer graphene (BLG) features several broken-symmetry metallic phases as well
as magnetic-field-induced superconductivity. The superconducting state is quite
fragile, however, appearing only in a narrow window of density and with a
maximum critical temperature $T_c\approx30$~mK. Here, we show that placing
monolayer tungsten diselenide (WSe$_{2}$) on BLG promotes Cooper pairing to an
extraordinary degree: superconductivity appears at zero magnetic field,
exhibits an order of magnitude enhancement in $T_c$, and occurs over a density
range that is wider by a factor of eight. By mapping quantum oscillations in
BLG-WSe$_2$ as a function of electric field and doping, we establish that
superconductivity emerges throughout a region whose normal state is polarized,
with two out of four spin-valley flavours predominantly populated. In-plane
magnetic field measurements further reveal a striking dependence of the
critical field on doping, with the Chandrasekhar-Clogston (Pauli) limit roughly
obeyed on one end of the superconducting dome yet sharply violated on the
other. Moreover, the superconductivity arises only for perpendicular electric
fields that push BLG hole wavefunctions towards WSe$_2$ -- suggesting that
proximity-induced (Ising) spin-orbit coupling plays a key role in enhancing the
pairing. Our results pave the way for engineering robust, highly tunable, and
ultra-clean graphene-based superconductors.
