Lets see...Any known force would require 10 times the amount of applied force to move the ball with 10 times the mass.
As well...since the balls are accelerating...a force would not only have to be applied 10 times the amount for the 10 kg ball...but such a force would have to be applied to a greater and greater extent to create acceleration.
Newtons law of gravity f = G m1 m2/R^2 tells us that the 10 kg ball WILL be pulled down with 10 times the force as the 1 kg ball...
Newton's second law F=MA tells us that a constant force applied to a fixed mass WILL result in constant acceleration...
Split, I'm totally open to new ideas, but they have to make sense; when they contradict basic physics principles then it's hard to take them seriously.