Oh it adds plenty of weight.  A buddy of mine had a similar replica and let me use it a couple of years back.  I thought it was heavy and gave it back so I didn't hurt myself.  After a few shots in the rain today, I was convinced this one is also heavy.  You would not want to give a huge heave on this bad boy!   I may have the main shaft a bit too long.  I am contemplating making a similar version with a shorter wooden shaft and then do some comparison shooting.  I also plan to make a third that has no stone at all and see how that all works.   After reading up on Indian Knoll's atlatls I am convinced this the purpose of a bannerstone- on the atlatl shaft. Now were they just for show or were they functional is another question.  Bob Perkins posted an article on line a few years back that suggests that wings help reduce the swishing noise volume and sound frequency so it is lower.   A silencer of sorts.  Stealth technology according to him.  
As heavy as this feels I have come to realize there is a lot I do not know.  I made a replica of an atlatl found at Council Hill Nevada and came to the conclusion that it was not a very good thrower.  It was about 20 inches long but was not more than 7/16" wide and the spur was terribly short.  My darts would barely fit on the spur.   Then a fellow atlatl enthusiast came to an event with these little 3-4 foot long darts.  They were almost arrows, and they worked GREAT in a smaller, thinner atlatl.  I tried the Council Hill replica and it was a dream boat to use.  The atlatl was fine.  I just needed lower mass darts.  My six feet long river cane darts were mammoth in size by comparison.  It never occurred to me to adjust my dart.  I will see if I can dig up a photo of that thrower to post.
Does this winged bannerstone atlatl seem heavy?  yeah.  Do I understand why?  no.  Will I?  If I keep workin' on it I might.  

  Feel free give me some of your thoughts.  I love the exchange.