This article proposes a new cooperative offloading protocol termed "user reciprocity" for backscatter communication (BackCom)-aided mobile edge computing (MEC) systems, whose quintessence is that each user can switch alternately between the active or the BackCom mode in different slots, and one user works in the active mode and the other user works in the BackCom mode in each time slot. Specifically, the user in the BackCom mode can always use the signal transmitted by the user in the active mode for more data transmission in a spectrum-sharing manner. To evaluate the proposed protocol, a computation efficiency (CE) maximization-based optimization problem is formulated by jointly power control, time scheduling, power reflection coefficient (RC) adjustment, and computing frequency allocation, while adhering to constraints on energy budgets, computing frequency thresholds, minimum computed bits, and harvested energy. To solve this non-convex problem, Dinkelbach's method and quadratic transform are first employed to transform the complex fractional forms into linear ones. Then, an iterative algorithm is designed by decomposing the resulting problem to obtain the suboptimal solution. For analytical insights, we not only provide some closed-form solutions, but also derive the analytical performance gain with reciprocal mode. Simulation results demonstrate that the proposed scheme outperforms benchmark schemes regarding the CE.