Entering atlatl weights into google search presents many pictures.
Weights varied greatly by region (or maybe better put , by"school" of making , by the influence available. ,and time allowed to fashion them.
The basics are , why a weight?
Then , where to mount it?
And of course , how to mount it.
Answers vary...
Here is a writing on the matter.
I'm not saying it is the right or wrong tell all.
And am certainly not saying it is the final say.
Only some example.
A search will help you build one. It is quite doable and not difficult to gain a more academic sense of their use and potential.
We had the advantage of sampling a variety ,and handling others.
Did not graduate to adding weights. But can imagine gaining some greater leverage/force of throw.
A simple shortcut after adding more traditional fletching ( like you would a well built arrow/dart ) was tying a couple large feathers at each end of each feather to create the required drag.
ATLATL WEIGHTS: Function and Classification. By William Perkins a.k.a. Atlatl Bob.