Dumb thought, but does a weighted ball help or hurt chances in this?
To me, a weighted ball either does everything it is supposed to do, or nothing it is supposed to do.
The reason why it does nothing it is supposed to do: the weight of the ball means that airflow is not raising the ping pong ball "up," unless the air pressure is turned up high enough. To me, that would mean that the heavier ball would sink closer to the bottom, and the ball is pulled up through suction force - this would mean that a different ball would be above the Rangers ball, and with less weight, this would make it easier for a different ball to be pulled.
However, the weight of a ping ping ball is also a direct factor in aligning the ball to go up the middle. Air flow and the combination of bouncing balls will move them around more. However, a weighted ball has two guarantees: #1, when air flow brings other ping pong balls near the weighted ball, the lighter balls will get bounced further away, as a result of having less mass. This means the weighted ball is less likely to stray far from the middle. #2, air flow in this case, is actually a good thing, because for a round, weighted object that still has enough pressure created on it for the object to rise - it will probably allow it to rise in a more controlled fashion as chaos goes on around it.
Sounds like one of these things that should be done as a Sports Mythbusters type of thing.