If Trump had been physically less obese and young enough he still wouldn't have had the ethical and emotional stability to even enter boot camp, nevertheless run for any office of the public trust.
Candidates for US Senate and for the Executive Branch should be required to pass a government Background Investigation before their name is placed on an Election Day ballot.
A cursory background check is required before recruits enter bootcamp. The least intrusive check requires honest completion of the SF-85, "Questionnaire for Non-Sensitive Positions" to initiate NACI investigations to support Low Risk positions. This de minimis requirement should be required for all political office candidated and its results made publicly available.
And candidate for high office including the presidency, should be investigated for their trustworthiness, reliability and competence to have access to sensitive information. At a minimum, such candidates should be required to complete the SF-86, "Questionnaire for National Security Positions", a form used to initiate the clearance process for High-Risk Public Trust positions and for all three levels of security clearances. It asks for personal identifying data as well as criminal records, illegal drug involvements, financial delinquencies, mental health counseling, alcohol related incidents and counseling, civil court actions, misuse of computer systems, and subversive activities for seven to ten years with some questions having no time limit.
Oddly, Trump and his daughter and Jared Kushner and others close to Trump lied on their SF-86 forms and after being required repeatedly to redo the application, managed to get access to information of all types that they could have mishandled or used for personal benefit. How in the world can anyone like that be permitted to run for high office or be connected to high office?
Then there's the emotional and mental stability factor. Can Congress require a definitive test for that? If there were an honest means to screen for that, certainly no one like Trump, a widely recognized candidate for a diagnosis of sociopathic and narcissistic personality disorders, would be judged qualified for office.