YankeeJim: Balance in a putter is what helps the putt stay on line. The more balance, the better the putter will swing and in this game that translates to the putt holding the line better.
I could never get my head around "balance helps the putt hold the line". Some magical quality that affects the roll after we hit it? Like "The Force"? Once the ball is rolling its path is determined by the slope(s), wind, and speed of the ball. Stay with me now!
ColumbusStorm's post might allow me to understand. If the speed of the ball is more consistent, and bhoese's precision tests show higher balance putters have less distance variance (for dings), then it follows that the path of the ball will be more consistent all other things being equal.
For the same putt, hit with same power on same line, a higher balance putter might have a distance variance +/- 6 inches. The speed of the ball along its path therefore must have a similar small variance. Therefore the path of the ball has a small variance. It holds the envisioned line better.