You're Correct!

The advice that you should accelerate your putter during the forward swing and through the impact area is sound in the sense that it advises against you decelerating the putter before impact.

However, it can also create another major problem in the fact that there is then a danger of you over-compensating and generating way too much speed and smashing your putt past the hole.

Take The Pendulum Test

The pendulum test is the perfect way for you to see the natural acceleration of your putter using the constant speed of the movement back and forth, and gravity. To take the test, you need to take hold of your putter at the top of the grip, holding it with your thumb and forefinger, and just let it swing back and forth. As you will see, the pendulum motion is identical to that of a grandfather clock. That natural acceleration is the key to great distance control on all of your putts. The longer the back swing, the faster the putter head accelerates in the forward swing, naturally allowing for the extra distance you need the further the length of your putt.

You now need to take this practice to the putting green. Find yourself a nice space on the green and place a tee in the ground. Take five steps and place another tee in the green. Every five steps you take, place another tee in the green until you have tees in the green to give you five different lengths of putt. You need six balls and start to hit putts to the different distances that you have set out. Try to keep the same constant tempo you saw when holding the putter with your finger and thumb throughout your putting stroke and not a conscious speeding up of the putter into impact. This will allow the length of your back stroke to dictate the distance your putt travels.

If your putter does not accelerate at all during your putting stroke then you can be sure that your stroke is decelerating. This action will cause you to leave your putts short of the hole. If you dont get your putts to the hole then you have no chance of getting it in the hole.

Buying a heavier putter may help you to a certain degree, but if you slow down the speed of the putter during your stroke then it will make no difference at all. You will still leave your putts short of the hole and your three putt percentage will still be too high.

Although we dont want the putter to decelerate during the putting stroke, if you accelerate too much then you will have a whole new problem. Too much speed in the forward stroke will see you hit most of your putts with no control and see them rolling way past the hole.