What is the authenticity and meaning of the hadith "The stomach is the home of all illness," and who narrated it?

What you asked about is not a prophetic Hadith (definition). Rather, it is from the wisdom of physicians. It was said that the first to utter it was Al-Harith ibn Kalada, and his complete saying is: "The stomach is the house of all illness, and abstinence is the head of all remedies." He also used to say: "What killed mankind and destroyed the predators in the wilderness is introducing food upon food before digestion." Others said: "If the inhabitants of the graves were asked, 'What was the cause of your demise?' they would say: 'Indigestion.'" The prophetic guidance in this regard is the most perfect guidance, for he (peace be upon him) said: "The son of Adam fills no vessel worse than his stomach. A few mouthfuls are sufficient for the son of Adam to keep his back straight. But if he must, then let one-third be for his food, one-third for his drink, and one-third for his breath." Ibn Rajab said: This Hadith is a comprehensive principle for all medical foundations, because the root of every disease is overeating.