The paper presents the realization of a Rydberg-dressed extended Bose-Hubbard model (eBHM) in a quantum simulator. The authors overcome experimental challenges to realize an effective one-dimensional eBHM, using a quantum gas microscope to probe the correlated out-of-equilibrium dynamics of extended-range repulsively-bound pairs at low filling and kinetically-constrained "hard rods" at half filling. Near equilibrium, they observe density ordering when adiabatically turning on the extended-range interactions. The results demonstrate the versatility of Rydberg dressing in engineering itinerant optical lattice-based quantum simulators and pave the way for realizing novel light-controlled extended-range interacting quantum many-body systems. The study highlights the potential for exploring various novel phenomena, such as non-local order, lattice supersolids, and exotic cluster Luttinger liquid phases, in the eBHM.The paper presents the realization of a Rydberg-dressed extended Bose-Hubbard model (eBHM) in a quantum simulator. The authors overcome experimental challenges to realize an effective one-dimensional eBHM, using a quantum gas microscope to probe the correlated out-of-equilibrium dynamics of extended-range repulsively-bound pairs at low filling and kinetically-constrained "hard rods" at half filling. Near equilibrium, they observe density ordering when adiabatically turning on the extended-range interactions. The results demonstrate the versatility of Rydberg dressing in engineering itinerant optical lattice-based quantum simulators and pave the way for realizing novel light-controlled extended-range interacting quantum many-body systems. The study highlights the potential for exploring various novel phenomena, such as non-local order, lattice supersolids, and exotic cluster Luttinger liquid phases, in the eBHM.