The president with the highest BMI is William Howard Taft.

Beside Taft, the presidents considered obese (BMI > 30) are Grover Cleveland, William McKinley, Theodore Roosevelt, and Donald Trump. The presidents considered overweight (BMI 25 to 30) are Chester A. Arthur, Bill Clinton, John Quincy Adams, James Buchanan, James Polk, Martin Van Buren, Rutherford B. Hayes, George W. Bush, Millard Fillmore, Zachary Taylor, Gerald Ford, Benjamin Harrison, Herbert Hoover, James Monroe, and George Bush.

The following is the list of US presidents with BMI of 25 or more:

PräsidentWeight (lbs)HeightBMI
William Howard Taft340 lbs6′46.6
Grover Cleveland260 lbs5′  11″36.4
William McKinley199 lbs5′  7″31.2
Donald Trump239 lbs6′  2″30.3
Theodore Roosevelt210 lbs5′  10″30.1
Chester A. Arthur224 lbs6′  2″28.7
Bill Clinton223 lbs6′  2″28.6
John Quincy Adams175 lbs5′  7″27.2
James Buchanan198 lbs6′  0″26.8
James K. Polk174 lbs5′  8″26.4
Martin Van Buren164 lbs5′  6″26.4
Rutherford B. Hayes175 lbs5′  9″26.2
George W. Bush191 lbs6′26.1
Millard Fillmore174 lbs5′  9″25.8
Zachary Taylor170 lbs5′  8″25.8
Gerald Ford190 lbs6′  0″25.7
Benjamin Harrison160 lbs5′  6″25.7
Herbert Hoover187 lbs6′25.6
James Monroe189 lbs6′  0″25.6
George H. W. Bush196 lbs6′  2″25.2

Sources:

https://potus.com/presidential-facts/presidential-weight/
https://www.statista.com/statistics/1108096/us-presidents-weights/
https://www.statista.com/statistics/1115255/us-presidents-heights/