  Rydberg tweezer arrays provide a versatile platform to explore quantum
magnets with dipolar XY or van-der-Waals Ising ZZ interactions. Here, we
propose a scheme combining dipolar and van-der-Waals interactions between
Rydberg atoms, where the amplitude of the latter can be greater than that of
the former, realizing an extended Hubbard model with long-range tunnelings in
optical tweezer arrays. For repulsive interactions, we predict the existence of
a robust supersolid phase accessible in current Rydberg tweezer experiments on
the triangular lattice supported by large-scale quantum Monte Carlo simulations
based on explicitly calculated pair interactions for ${}^{87}$Rb and with a
critical entropy per particle $S/N \approx 0.19$. Such a lattice supersolid is
long-lived, found over a wide parameter range in an isotropic and flat
two-dimensional geometry, and can be realized for 100s of particles. Its
thermodynamical and dynamical properties can hence be studied at a far larger
scale than hitherto possible.
