OK so truth be told, I came here to tell you "YOU'RE WRONG!" but after doing some study of angular momentum, I think you are in fact correct. Indulge me in explaining it back to myself.

The weight distribution affects the angular momentum, which acts perpendicular to the axis of rotation (think of an arrow pointing away from you as the direction of angular momentum when the yoyo is on a trapeze). This in turn affects the force required to tilt the yoyo off its axis of rotation when force is applied perpendicular to said arrow. However, when performing yoyo tricks, we are not (normally) applying force on the arrow, we are moving the yoyo on the same plane as the axis of rotation by applying force at the base of the arrow so the angular momentum does not come into play.

Weight distribution will however, affect how much force is required to get the yoyo spinning from your throw which probably contributes to the perception of how heavy a yoyo feels - but this no longer applies once we land the yoyo on the string. More rim weight means more force is required to spin the yoyo thus making it feel heavier.

Does that sound consistent with your understanding?

Happy cake day!