Definition of "Sport:"
"an activity involving physical exertion and skill in which an individual or team competes against another or others for entertainment."
Now, when looking at each individual component of the above definition, bodybuilding would classify as a sport.
--Bodybuilders exhibit physical exertion when lifting weights and it does take a certain amount of skill to successfully deadlift or squat.
--Bodybuilders (individuals) do compete against each other for entertainment.
The "downside" is that the physical exertion and/or skill does not take part at the same time they are competing against each other. So, in that regard, bodybuilding would not be a sport.
This is a great dilemma.