Balance on the tennis court means having your weight evenly distributed over both feet. Leaning in any direction means you are not balanced.
It is important to be balanced as quickly as possible after you hit the ball, as well as just prior to your opponent's hit. Many times after hitting a ball on the run, it is difficult to regain this balance. Use the split-step to help stabilize your movement and redistribute your weight directly over your feet. This will give you the ability to react in any direction just after the ball is hit.
Remember that the best movers on the court also have the best balance. Most are very fast but they are also very quick to react because their ability to be balanced allows them to go in any direction just after the opponent hits the ball.
Try to pay attention to your weight distribution more often on the court. The better you get at keeping and regaining your balance, the better you will be able to react and move to the ball.