Weightlifting is still for most of the world the ability to lift weights overhead in the two classical lifts i.e. the snatch and the clean and jerk. Despite what powerlifters say weightlifting is a better measure of starting strength, explosive strength, full body flexibility and vertical jump. Everybody prefers watching a human against a weight rather than a powerlifter wrapped up in yards of denim doing quarter range of motion squats and shirt presses with a dozen spotters.
Bodybuilding is an activity in which steroids + nutrition is the biggest determinant of success. Bodybuilders spend more time discussing drug regimens and diet tips than technique, periodization, intensity and cycling. Which leads me to conclude that bodybuilding is even further away from being called a sport than hot dog eating contests.