With less than eight weeks until Election Day and pressure mounting for the candidates to give details about their health and medical histories, Donald J. Trump acknowledged on Wednesday that he was overweight and taking a cholesterol-fighting drug, and Hillary Clinton elaborated on the circumstances that led to her contracting pneumonia and the medicine she was taking to recover.

Mrs. Clinton’s doctor said she “continues to improve” after contracting a “mild, noncontagious” form of pneumonia diagnosed on Friday, two days before she grew dizzy and was seen losing her footing while leaving a ceremony for the 15th anniversary of the Sept. 11 terrorist attacks.

In a letter released by the Clinton campaign, the physician, Dr. Lisa R. Bardack, said she had evaluated Mrs. Clinton several times since Sunday, including on Wednesday. “She is recovering well with antibiotics and rest,” Dr. Bardack said. “She continues to remain healthy and fit to serve as president of the United States.”

After Mrs. Clinton left Sunday’s Sept. 11 ceremony early, a spokesman initially said only that she had felt overheated. But after video shot by an onlooker showed Secret Service agents helping a wobbly Mrs. Clinton into a van, her campaign released a statement from Dr. Bardack saying that Mrs. Clinton had pneumonia.