In the first step, a 1-DOF power-assist robotic system (PARS) is developed for lifting lightweight objects. Dynamics for human-robot co-manipulation of objects is derived that considers human cognition (weight perception). Then, admittance control with position feedback and velocity controller is derived using weight perception-based dynamics. Human subjects lift an object with the PARS, and HRI (human-robot interaction) and system characteristics are analyzed. A comprehensive scheme is developed to evaluate the HRI and performance. HRI is expressed in terms of physical HRI (maneuverability, motion, safety, stability, naturalness) and cognitive HRI (workload, trust), and performance is expressed in terms of manipulation efficiency and precision. To follow the guidance of ISO/TS 15066, hazard analysis and risk assessment are conducted. A constrained optimization algorithm is proposed to determine the values of the control parameters that produce optimum HRI and performance with lowest risk. Results show that consideration of weight perception in dynamics and control helps achieve optimum HRI and performance for a set of hard constraints. In the second step, a weight perception-based novel variable admittance control scheme is proposed as an active compliance to the system, which enhances the physical HRI, trust, precision and efficiency by 53.05%, 46.78%, 3.84% and 4.98%, respectively, and reduces workload by 35.38% and thus helps achieve optimum HRI and performance for a set of soft constraints. The risk reduces due to the active compliance. Then, effectiveness of the optimization and control algorithms is validated using a multi-DOF PARS for manipulating heavy objects, and intuitive and natural HRI and performance for power-assisted heavy object manipulation are achieved through calibrating HRI and performance with that for manipulation of lightweight object.