Soft continuum manipulators, inspired by nature, facilitate motion within complex environments where traditional rigid robots may be ineffective. This has driven demand for new control schemes designed to precisely control these highly flexible manipulators, whose kinematics may be sensitive to external loads, such as gravity. In this paper, published in the International Journal of Robotics Research (IJRR), we propose coupling Cosserat rod-based modelling with integrated sensing and efficient numerical determination of the Jacobian matrix at each time step to deliver practically viable, real-time closed-loop control for our waterjet-actuated soft continuum manipulator (the HydroJet). Using this control approach, we demonstrate a reduction orientation error and increased system stability, even under the influence of gravity. The stable closed-loop path following, as demonstrated, has the potential to enable semi and fully autonomous manipulation tasks in the next generation of soft continuum robots actuated via a follower wrench and experiencing external loading.