Okay, this question deserves an answer, but hasn’t gotten one yet. I’m not a historian, but Theodore Roosevelt is one of my favorite people, so I’ll try to answer this mostly on background.

I always imagine him talking really quickly, almost twitching whenever he needed to sit still

This is, basically, the correct impression. Roosevelt is often described as extremely active with almost frenetic energy directed toward mental, physical, or social activity. He was known for bounding up staircases (both in front of the New York Civil Service Commission and the Albany statehouse), the rapid pace of his speech and conversation (punctuated by forceful gesticulation and high-pitched laughter), and frequently brought friends and visitors on long endurance-based outdoors activities. He could sit still when he wanted and was an avid reader and prolific writer.

Was TR a healthy man?

The answer to this question depends largely on the period of his life one wishes to discuss. For much of his adult life Roosevelt was a healthy and reasonably fit person. His early childhood, however, was largely defined by recurrent and persistent illness. This primarily manifest as fever, respiratory issues and asthma, and a weak digestive system that the family dubbed “cholera morbus.” In addition, Theodore was often described as small, thin or wiry, and had very poor eyesight (which went undiagnosed until he was about 14).

The origins and causes of Theodore’s condition are not really known. Some have simply concluded that he was a frail child, prone to illness, which makes tales of his later physical prowess that much more impressive. David McCullough has made a pretty stirring case that Theodore’s ailments are tied directly to anxiety stemming from the frequent absences and sometimes strict bearing of his father, Theodore Roosevelt, Sr., whom Theodore idolized throughout his life.

On or about his 12th birthday, after visiting yet another doctor in regard to his illnesses, Theodore Sr. famously told his son, “Theodore, you have the mind but you have not the body… You must make your body. It is hard drudgery to make one’s body, but I know you will do it.” (Letter from Theodore Roosevelt St to his daughter Bamie, 9/6/1870 (Theodore Roosevelt Collection, Harvard University)). Roosevelt then legendarily took up an intense fitness regimen consisting of weightlifting, boxing, calisthenics, horseback riding, and other activities. From this point on, Theodore was largely the energetic, active, outdoorsman prone to hurly burly that he is so often characterized as. However, he would never entirely shed them and continued to have the occasional bout of “cholera morbus” during times of intense stress or when affected by other illnesses.

Outside of these general ailments, Roosevelt was physically impressive, described as around 5 foot 9 and mostly muscle. He ate like a madman, which led him to packing on the pounds whenever he failed to maintain a sufficiently active lifestyle. While he weighed in at 135 pounds during a boxing competition at Harvard, he would regularly exceed 200 pounds in later life. Roosevelt’s constant activity and derring-do led him to suffer numerous injuries and ailments in his adult life (a leg injury from having his carriage was struck by a train while campaigning, a gunshot to the chest, a malarial fever acquired in Brazil, blindness in one eye resulting from a boxing injury, etc.) These accumulated injuries would weaken Roosevelt substantially and contribute to his early death in 1919.

How did his diet and exercise regimen affect his politics?

For this, I can’t really say that there’s a clear answer. I would venture it more likely that Roosevelt’s philosophy of life and politics is reflected in his exercise regimen than the other way around. He was an ardent proponent of individual responsibility, national self-determination, and civic responsibility. I would argue that these same preferences are what drove him to “make his body” and lead the life that he did.

Sources are primarily Edmund Morris’s exceptional three-part biography, David McCullogh’s Mornings on Horseback, and Wagenknecht’s Seven Worlds of Theodore Roosevelt.