Does the bleeding time depend upon whether the subject is fat or thin?

no

Obesity or lack of it does not affect bleeding time. By the way, bleeding time is an obsolete test. For healthy diet: http://www.choosemyplate.gov/., exercise 30 minutes/day, drink enough water daily so your urine is mostly colorless, have safe sex, no tobacco alcohol weed or street drugs. Get HPV and Covid vaccines. Wish you good health!

Bleeding time is usually not related to body size.