This paper presents a novel method to maintain the dynamic balance of a Mobile Manipulator (MM) during the pick-up of heavy objects. The approach entails the generation of a preliminary reach-to-grasp trajectory, which is subsequently refined by an Optimization-Based Controller (OBC) formulated as a Quadratic Program (QP). The trajectory is modified in a minimal fashion to ensure that the robot maintains balance during the reaching phase and remains balanced when the payload is grasped. This is accomplished by incorporating a balance constraint into the OBC that predicts the Zero Moment Point (ZMP) position of the robot at the beginning of the pick-up phase. This accounts for the gravitational and inertial effects that the object has on the robot. The method is validated through simulations conducted with the TIAGo robot in Gazebo. The results demonstrate that the proposed approach effectively prevents the robot from tipping over when the payload is considered.