General

Is it possible to be fat and healthy. Is it possible to me medically obese, meaning being based off of the bmi system, and healthy.

It depends. Fat is not a 100% guarantee for bad health, it is a risk factor. It doesn't necessarily cause problems, it might just increase the chances for them to appear.

Just like smoking is a strong risk factor for lung cancer, but here are young people who never smoked and get lung cancer, and there are chain smokers who live to 90 years without having such problems. Still, it changes the odds.

I've seen people with relatively little extra weight suffering from it medically, and also people almost wider than tall without health problems.

The other responses are good.

BMI is simply a function based on weight vs. height. It says nothing about what the weight consists of.

Not saying you should slave away at the gym, but bodybuilders are often "overweight" or even "obese" based on weight.

Also, a lot of football players, volleyball players, softball players, etc. are heavy. In high school, I was often mesmerized by how thick the volleyball players were, although looking back many were a bit thinner than I would have really preferred.

I think the worse thing is if you aren't at least somewhat active. Not saying you should be able to run a marathon, but.. you should be able to drive a car for 10-12+ hours on one day, be able to walk across a supermarket or shopping mall, and be able to hang out at a park. A 5 block walk shouldn't scare you. I also expect you to be able to carry a 40 lb box up 3 flights of stairs.