Why do you stop losing weight after you hit a certain point in your diet even though you keep the diet and continue to play sports?

Everybody's different. But, if you do the same exercises in your workouts, your body adjusts to the workout. You need to change your workout to shock different muscle parts. Of course, I must advise to consult a physician depending on your health status. Changing the intensity level also helps kick your metabolism up at resting rate. I'm not sure what diet you are on, but a good diet is one you would consider just a part of your healthy lifestyle. I, myself have been on the greek mediterranean diet and love it. Good luck on losing more weight, hope that helps.

That is the point at which you reach balance. Your body is at the point where the energy it takes in is exactly the same as the energy it uses, so no more weight is lost and no more is gained. You should doublecheck that you do not need to lose more weight: if not, then congratulations! If you do, then you should simply do slightly more exercise and eat slightly less.