Does a heavier grip make a lower swing weight?

Interesting…. was going through the threads on this topic
Context: I got a N9II (black-pink), added an over grip, it played as I expected , not too heavy , medium flex, easy clears. I added one more layer “thinking comfort” and the racket all of the sudden felt heavy and stiff like a plank.
I have a BS12 3U which has 2 over grips but it never felt this way, it still plays med-flexy, easy control (change of direction) and I feel grip size is larger on the BS12 than N9II
Interesting how just a grip changes bp, overall weight, swing etc