So your definition of sport is "an activity that makes the player perspire", and by extension the best player is "He or she who perspires most". Mmmm - I think we all know where you are coming from.
Dictionary.com defines sport (in part) as:
1. an athletic activity requiring skill or physical prowess and often of a competitive nature, as racing, baseball, tennis, golf, bowling, wrestling, boxing, hunting, fishing, etc. 2. a particular form of this, esp. in the out of doors. 3. diversion; recreation; pleasant pastime.
There are plenty of players of baseball, football, hockey & swimming at the top of their respective games carrying a few extra pounds. Physical attributes are only important insofar as they limit or otherwise the activity.
So … you just keep buying those headbands and deodorant.