Dear Jeff,
The heavier putter, having more mass, has more "send" for the same putter head speed at impact. This encourages a slower putter head speed on the same speed greens.
But, in pendulum physics, the mass factor cancels out of the motion equation and is theoretically insignificant in the putting tempo. I teach people to swing a short piece of hollow copper tubing to smooth out the rocking up and down of the shoulder-frame without regard to hefting a putter head back off a static position on the ground at address.
Even with that said, though, the momentum of the putter at rest, in the back-stroke coasting to a stop at the top, transitioning from back-stroke to down-stroke, peak strain on the arms at the bottom of the stroke, and coasting up to a stop at the top of the follow-thru are all instances where a certain mass in the putter head helps define the contrast between good and bad motion. If the putter is too light, the putter momentum does not effectively signal the inside of the hands in the grip about poor motion patterns.
In addition, a certain heaviness is good to encourage quiet hands and to discourage lifting with the hands, wrists, or elbows -- leaving the heavy putter and "heavy" hands extended down the same extent throughout the stroke.
Part of the problem is comparing the massiveness of the putter to the golfers inertial properties in his hands and forearms, his innate strength, and his sensitivity to mass differences. Another part of the problem is that the human body has a comfort range in the stroke in which the stroke is long enough not to baby the putt but not too long to challenge balance and head-eyes and stroke biomechanics; this comfort stroke range needs to be fitted with a putter mass that works well with the characteristic green speeds and putt lengths the golfer faces.
Some pros change the putter weight to fit the green speed to keep a 10-foot putt having the same stroke amplitude, even though the green speed differs from course to course. I don't like this approach, but the general notion of fitting the putter to the green is sound -- it's just that the putter mass needs to fit the physiology and tempo and comfort range of the golfer as well as the typical green speeds and typical putt lengths.
Cheers!
Geoff Mangum
Putting Theorist and Instructor
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