Just to add to your point about BMI.
I am currently Obese (I want to lose some weight). However, I once got myself to the point of having a BMI of 25. I looked emaciated, I could count my ribs through my skin, people were concerned about my health. When I started putting weight back on, I had a specialist at a hospital advise me that my BMI was unhealthy and that I should lose weight. I had a BMI of about 28.
This is a common problem in my family.