A control algorithm is developed to enable dynamically stable spherical-wheel robots (ballbots) with arms to detect a heavy object of unknown mass, navigate to it, lift it, transport it, and place it in a desired location semi-autonomously. Previous work has successfully demonstrated two-wheeled dynamically stable mobile manipulator robots transporting heavy objects. We report here the first ballbot to reliably achieve such a task. A successful semi-autonomous lift and transport of a 15 kg heavy box whose actual mass was unknown was achieved using a combination of feedforward and feedback control laws based on a quasi-static center of mass computation. The ballbot's pan and tilt sensor turret tracked fiducial markers on the box. Ballbot-to-human and human-to-ballbot exchanges of a 10 kg heavy object was achieved while dynamically balancing.