The doctor acknowledges the fact that being overweight has long been linked with a variety of health problems. She just goes on to conclude that being slightly overweight is sufficient for being healthy.

The doctor never defines the term “healthy,” but she doesn’t need to. So (B) doesn’t describe why her reasoning is flawed.

The doctor is talking about being overweight and underweight; she doesn’t address appropriate weight at all. Either way, this doesn’t affect her argument; she’s likely aware that appropriate weight varies from person to person.

The doctor never makes a claim about “a property that would suffice to make a person unhealthy,” much less claim that lacking such a property would make one healthy. Instead, she makes a claim about a property that would suffice to make one healthy— being slightly overweight.

The author mistakes a merely relative property— being healthier than someone else— for one that is absolute— being healthy. But a person could still be slightly overweight and unhealthy, even if they're healthier than someone who's very underweight.