The biggest difference I have noticed when drawing heavy and light cue balls is that it seems the light ball will hesitate in place just spinning before rolling backwards and the heavy ball seems to draw immediately after object ball contact. I suppose it could be due to cloth also but it always seems consistent with the heavy ball.
I wonder if the weight is allowing the spin to kick in faster on slow spin draw - i.e. minimal draw. If you power draw it might spin a bit but with light draw it spins less and with the added weight of the heavier cue I wonder if the spin affect is more immediate due to the weight?
Just thinking out loud.