Recommendation systems effectively guide users in locating their desired information within extensive content repositories. Generally, a recommendation model is optimized to enhance accuracy metrics from a user utility standpoint, such as click-through rate or matching relevance. However, a responsible industrial recommendation system must address not only user utility (responsibility to users) but also other objectives, including increasing platform revenue (responsibility to platforms), ensuring fairness (responsibility to content creators), and maintaining unbiasedness (responsibility to long-term healthy development). Multi-objective learning is a potent approach for achieving responsible recommendation systems. Nevertheless, current methods encounter two challenges: difficulty in scaling to heterogeneous objectives within a unified framework, and inadequate controllability over objective priority during optimization, leading to uncontrollable solutions. In this paper, we present a data-centric optimization framework, MoRec, which unifies the learning of diverse objectives. MoRec is a tri-level framework: the outer level manages the balance between different objectives, utilizing a proportional-integral-derivative (PID)-based controller to ensure a preset regularization on the primary objective. The middle level transforms objective-aware optimization into data sampling weights using sign gradients. The inner level employs a standard optimizer to update model parameters with the sampled data. Consequently, MoRec can flexibly support various objectives while maintaining the original model intact. Comprehensive experiments on two public datasets and one industrial dataset showcase the effectiveness, controllability, flexibility, and Pareto efficiency of MoRec, making it highly suitable for real-world implementation.