The thought experiment: How fat do you have to be to stop a bullet?
Don't count on the fat in your body protecting you from bullets.
It depends on the gun

Experiments using ballistic gelatine to mimic the human body suggest that a 9mm bullet from a handgun will penetrate about 60cm through human fat tissue. A fully jacketed bullet from an assault rifle, such as an AK-47, will go much further and can easily shoot through a brick wall.
Nobody is that fat

A morbidly obese person weighing over 125kg might have 60cm of fat at the thickest point, including subcutaneous fat and the fat that surrounds their organs. But no one has that thickness evenly across their entire body. Even a blue whale’s blubber is only 30cm thick.
Do you feel lucky?

In 2010 Samantha Lynn Frazier was hit by a stray bullet in a shooting in Atlantic City, New Jersey. The bullet lodged in her ‘love handles’ and she was otherwise unharmed. This is rare, though, and we can’t know for sure whether the bullet ricocheted off something else before it struck her!
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