So does swinging a heavier bokken prove anything?
prove that you can swing a heavier bokken.
try light up on the grips, if you knuckles turn white after awhile, you are gripping to tight. try bring the bokken up, with minimal amount of muscle, then let it drop (don't even think of cutting). see if the tip waving or not. if it is then you have tension in various parts of your arms and shoulders and the rest of your body. did your sensei tell you that you should be cutting with your body, not your arms?