Well, not being fat doesn't mean you are fit, but being fat is certainly incompatible with being fit. I speak as a fat guy who's probably less unfit than 95% of people at my weight (over 320 lbs): I'm still not "fit".
Seems like weight should be considered one indicator of fitness but not the most important one.
I'm not sure if that's cruelty or awesome on the part of your parents. I'm leaning towards awesome.