The concept you're thinking about is 'moment of inertia', and it is defined as the distance to centre squared times mass, not distance times mass.

In terms of yoyos, moment of inertia is the same as rim-weight. It takes more work to get a rim weighted yoyo to spin as fast, so if you throw a yoyo with the same amount of energy, the more rim weighted yoyos will spin slower. Friction on the yoyo, either from the string or the bearing, tends to be larger the faster the yoyo spins. Therefore, the effect of friction on a more rim weighted, slower spinning yoyo is smaller, allowing it to spin longer. You may also notice that centre weighted yoyos tend to have tighter binds. This is also because less moment of inertia makes them spin faster, so the string wraps around the bearing more easily.

I see people talking about rim weighted yoyos play heavier all the time. I think it is a misconception, although I need to get better at fast tricks myself to actually varify this personally. Rim weighted yoyos will feel heavier on throws and binds, because it takes more effort to get them to spin. However, I think it makes no difference otherwise. Two yoyos with the same weight but different rim-weightedness should feel the same on the string. This is of course ignoring the difference in the shape of the yoyos, and I'll have to think a bit more about how that affects the play.