As far as the number of wheel weights on your kawi.... there is no number. It depends how many it needs in order to balance it.
One of the guys here mentioned that you could have spun the tire. What that means is that you you spin the tire on the actual wheel. So now, instead of having the appropriate location for the balancing weights, they could be in the wrong spot...... or.... you might have just lost some of the weights. At very high speeds this would be more noticeable.
Also, if you are riding an old stock ZX-6R shock.... that could be part of the problem too.... but dunno if it would show those symptoms on a straight.
FYI - (and you might know this) chattering in the racing sense of the word is typically seen on the FRONT end under braking, but I know you are just trying to describe what was happening.