Not sure if everyone would be familiar with the concept, but in situations where you need to gear an engine but can’t/don’t want to have a gearbox, you can use roller weights. A simple way of how it could be used in yoyos is below. This view is of one yoyo half which is then cut in half down the middle. In reality, I think you’d need more chambers to keep it smooth, but whatever.
So, each of the black rectangles is a chamber just large enough for the little silver ball bearing (the weight). Each chamber also contains a spring that in rest state holds the weight to the inside edge of the chamber. However, as the yoyo spins, the spring would be tuned to allow the weight to move further and further out toward the edge. This is effectively a “geared” yoyo.
The benefit? Well, there’s 2 factors when it comes to inertia in yoyos. One, spin speed. Two, weight distrubution. With a small throw, you can get high spin speeds, but you can’t get the advantageous rim weighted distribution you might with a larger, heavier throw. On the other hand, large and heavy throws don’t spin as fast. But, the geared yoyo should, in theory, be able to do the best of both.
On a throw, the weights will be toward the inside of the yoyo promoting acceleration like that of a small diameter throw. But, as the throw reaches max speed, the weights will then move (and stay) outward to keep that spin going much longer. Finally, when the spin of the yoyo begins to decrease, and the outward weight distribution is becoming and less and less effective, the weights again start moving back toward the inside. This once again promotes spin speed to milk that last bit of energy from the spinning yoyo.
Obviously this is totally theoretical and I’m not sure you would actually see a practical effect. But, if it did work, you might end up with an incredibly long spinning and stable yoyo.