Weight-perception-based fixed admittance control algorithm and variable admittance control algorithm are proposed for unimanual and bimanual lifting of objects with a power assist robotic system. To include weight perception in controls, the mass parameter for the inertial force is hypothesized as different from that for the gravitational force in the dynamics model for lifting objects with the system. For the bimanual lift, two alternative approaches of force sensor arrangements are considered: a common force sensor and two separate force sensors between object and human hands. Computational models for power assistance, excess in load forces, and manipulation efficiency and precision are derived. The fixed admittance control algorithm is evaluated in a 1-degree-of-freedom power assist robotic system. Results show that inclusion of weight perception in controls produce satisfactory performance in terms of power assistance, system kinematics and kinetics, human–robot interactions, and manipulation efficiency and precision. The fixed admittance control algorithm is then augmented to variable admittance control algorithm as a tool of active compliance to vary the admittance with inertia instead of with gravity. The evaluation shows further improvement in the performance for the variable admittance control algorithm. The evaluation also shows that bimanual lifts outperform unimanual lifts and bimanual lifts with separate force sensors outperform bimanual lifts with a common force sensor. Then, the results are proposed to develop power assist robotic systems for handling heavy objects in industries.