This work explores a cooperative wireless powered communication network (WPCN) aided by multiple backscatter devices. In this work, for the envisioned hybrid user scenario, we maximize the weighted sum throughput under a joint set of constraints in the time allocation parameter, a set of reflection coefficients of backscatter devices, and the constraints for meeting the successive interference cancellation threshold requirements. Henceforth, we investigate various sub-problems and propose our solution to the formulated non-convex optimization problem. Finally, using extensive numerical simulations, we observe that the hybrid NOMA-plus-TDMA scheme outperforms a few benchmark and existing conventional schemes for our considered system model.