I use bannerstones on my basketmaker-style atlatls. Here is my Dad's:
My little Brother's:
Both are about 2 inches long.
Other styles of atlatls may hold up better to being used as melee weapons, but some are just too fragile. Also, the weight--as I've used it, and seen it used--is fastened securely near the handle end. Even a small weight like these, when it comes loose and slides to the top as you throw, will just about jerk the atlatl out of your hand.
Now this is my opinion, and as such should be considered the Doctrine of K'Jev and taken as such (as an opinion), but the idea of a large weight on the end of your atlatl would make it much harder to throw, and much harder on your arm.
On the other hand, try it, film it, and post it, and see what happens.