F=ma is only that simple to calculate when the yoyo is moving in a straight line, which is rarely the case in yoyoing. Like kadabrium said in the other thread, once the yoyo starts moving in more circular patterns, then rotational physics start to apply. The form of Newton’s law that you would want to use there is: τ = Iα
As an illustration of this: the length of your string can also affect how fast you can play. If you’ve never tried comparing long strings to short strings, you can see the basic effect easily by swinging a yoyo around in a circle on the end of the string. If you swing the yoyo from the end of the string, and then grab the string halfway up and swing it in a circle again, it accelerates differently even though the mass of the yoyo doesn’t change (the mass of the string does change, but by a negligible amount). That’s because the moment of inertia does change when you move the mass closer to or further from the center of rotation (the same reason rim-weighting affects how long a yoyo will spin).
Changing the weight distribution of a yoyo changes its moment of inertia, so it does have an effect on how the yoyo will accelerate in a circular path given a set amount of force. It’s just a matter of how much difference it actually makes, which is kind of hard to work out on paper because measuring (or looking up) moment of inertia is harder than measuring mass, and the calculations would depend on other factors such as the radius of the circular path of the yoyo. So, there is theoretically an effect, but it’s possible that it is too small for most people to notice. Or it might not be, I have no idea.
Practically speaking, I agree with those saying that how the weight distribution affects how well the yoyo handles speed is also important. If two yoyos should theoretically have the same acceleration under the same conditions, but one requires more effort to keep under control and to maintain spin when playing at higher speeds, that is going to have a practical effect on how fast someone can play with it and how fast they perceive it to be. For example, Mosquitos are really light, but I find them kind of hard to play fast with. That depends a lot on the skill of the person using the yoyos, though, so it won’t necessarily apply to everyone the same way.