  Neutral atom arrays have emerged as a versatile platform towards scalable
quantum computation and optimization. In this paper we present first
demonstrations of weighted graph optimization on a Rydberg atom array using
annealing with local light-shifts. We verify the ability to prepare weighted
graphs in 1D and 2D arrays, including embedding a five vertex non-unit disk
graph using nine physical qubits. We find common annealing ramps leading to
preparation of the target ground state robustly over a substantial range of
different graph weightings. This work provides a route to exploring large-scale
optimization of non-planar weighted graphs relevant for solving relevant
real-world problems.
