Generally, counter weighting of putters was (and is) used as a way to manipulate the head feel and overall feel of the putter. As putter heads have become heavier, some players will counterweight to dial in a head feel and overall feel they like. Others like the heavier head feel and will not counterweight. In many cases, counter weighting comes naturally when a company produces a putter with a long, or oversize grip that weighs more than traditional putter grips. In the old days, putter head were 320-325 grams and grips were 45-50 grams. Today, most “standard” putter heads are at least 350 grams and many are heavier than that. Putter grip weights can range from around 50 grams to 125 grams or more. Heavier grips require heavier heads to maintain head feel for most players.
The by-product of a heavier head AND grip, thus producing a heavier overall weight putter, is that for most players it allows them to produce a more consistent and smoother stroke. Anti-Yip putters that have been produced in the past were nothing more than heavy heads (400 gram +) with large heavy grips. This set up makes those involuntary “jerks” or “yips” go away for most people. The overall weight of the putter and the large grip engages the large muscles, preventing the small twitchy movements in a stroke that result in “the yips”. I have always contended that the reason the Belly and Long phenomenon was so successful for many players was that those types of putters required much heavier heads to offset the longer lengths and heavier grips that were used. the technique might have had a little to do with it, but the weight distribution in those putters was the primary reason they worked, in my opinion.
It really is a personal choice on whether you need to counter weight a putter or not. If you do, realize that heavier weight on the grip side usually requires heavier weight on the head side to maintain a good head feel.
Hope this helps.