I didn't have the time to completely answer, I mostly just wanted him to know that he shouldn't listen to you when you say that F=mA is relevant.
Look up the equation at the bottom of this page:
http://www.real-world-physics-problems.com/elastic-collision.html Or look at Dr. Dave's explanations...which have been posted ad infinitum on these boards.
Yes, a faster moving lighter cue may provide more speed on the cueball than a slow moving heavy cue.
Yes, for breaking, a lighter cue is likely better.
The OP is asking about playing and I can't say that I've seen any evidence that it matters.
They used to say that they used heavy cues before worsted wool because the heavy cue moved the ball easier, but that is only if the contact velocities stay equal.
Again, Rick, I'm likely to call you out on everything that you post when you obviously have little or no clue about the subject. Hopefully nobody will seriously injure themselves with an exploding car battery charger if I do that.