In this paper, we propose a novel vision-based control algorithm for regulating the whole body shape of extensible multisection soft continuum manipulators. Contrary to existing vision-based control algorithms in the literature that regulate the robot's end effector pose, our proposed control algorithm regulates the robot's whole body configuration, enabling us to leverage its kinematic redundancy. Additionally, our model-based 2.5D shape visual servoing provides globally stable asymptotic convergence in the robot's 3D workspace compared to the closest works in the literature that report local minima. Unlike existing visual servoing algorithms in the literature, our approach does not require information from proprioceptive sensors, making it suitable for continuum manipulators without such capabilities. Instead, robot state is estimated from images acquired by an external camera that observes the robot's whole body shape and is also utilized to close the shape control loop. Traditionally, visual servoing schemes require an image of the robot at its reference pose to generate the reference features. In this work, we utilize an inverse kinematics solver to generate reference features for the desired robot configuration and do not require images of the robot at the reference. Experiments are performed on a multisection continuum manipulator demonstrating the controller's capability to regulate the robot's whole body shape while precisely positioning the robot's end effector. Results validate our controller's ability to regulate the shape of continuum robots while demonstrating a smooth transient response and a steady-state error within 1 mm. Proof-of-concept object manipulation experiments including stacking, pouring, and pulling tasks are performed to demonstrate our controller's applicability.