Im not sure what you mean by under eating, but eating fewer calories than you spend is the only way to lose fat, other than surgery.
Dictionary definition "above a weight considered normal or desirable."
The WHO definition "a BMI greater than or equal to 25 is overweight"
Not sure what definition you use, most gym-heads are technically overweight.
But discussing semantics is not the topic here.
BMI is a tool applied to populations, used on individuals it can be very inaccurate, which is why nobody does it outside of blogs and magazines.
You're wrong. The typical diagnostic method for overweight and obesity (BMI) does not differentiate between muscle and fat, because mechanisms that do are too expensive/complex for the use, but the term, in fact, does.
At their most basic, the words “overweight” and “obesity” are ways to describe having too much body fat. [0]
Overweight and obesity are defined as abnormal or excessive fat accumulation that may impair health. [1]
[0] http://www.hsph.harvard.edu/obesity-prevention-source/obesit...
But I do concede, overweight in that context does refer to excess fat.