A person who cares about his/her health and wants to have a long life should definitely carry out the following advice of the Prophet (PBUH).

"A few morsels are enough for a person to live.” “A person who wants to eat more (In order to become stronger and to work harder) should fill one third of his stomach with food, one third with water and should leave the remaining one third empty in order to breathe easily.” (1)

Researches show that for deep and easy breathing the stomach should not be full. Not being able to breathe fully means not being able to live fully. Besides, the blood that comes to the lungs to be cleaned spreads to the body without being cleaned completely. Thus the health of a person deteriorates. What cleans the blood is the oxygen taken into the lungs through breathing. This is possible by breathing deeply. A part of the stomach should be left empty for breathing deeply.

A person breathes about 16 times in a minute. He/she takes in half a litre of air with each deep and full breath.

So a person takes 16x60 minutes x 24 hours = 23.240 breaths; 23.240 x 1/2 = 11.620 litres of air in a day.

What cleans our blood is the oxygen contained in the 11.620 litres of air. If we fill our stomach with food, there will be no space for the lungs to inflate in the abdomen; so we will breathe half. Therefore, the oxygen taken into our lungs through air decreases to half. It will not suffice to clean the blood and our health deteriorates. The food that we buy with the money we work hard to earn and that we work hard to cook gives us harm instead of use. The Prophet (PBUH) expressed how bad and harmful it was to eat until we fill up the stomach by saying the following sentence:
"Man never filled a container worse than his stomach." (2) That is, the worst thing a man fills is eating by filling up his stomach.

References:
1. Ibn Majah, Et'ime, 50
2. Tirmizi, Zühd, 47