Why do the bigger plates on Earth tend to have the highest movement velocities?

They have more mass, inertia and momentum and force is why. Once they are moving the only thing that can slow them down is ramming into another continental plate, which is exactly what is happening with India,and Asia. This is why the Himalayas are the highest mountains on Earth and has some of the highest magnitude earthquakes. India is still subducting underneath Asia so the frantic crust is getting sliced off and crumpled up. Something similar is going to happen between Africa and Europe. West Africa is,subducting underneath Europe and the Mediterranean will close up.

Remember, plate motion is judged relative to the other plates. If a given plate is bigger, it will appear to be moving faster than the others, because more of it is covering the same average distance in the same average time as the smaller plates--much like the edge of a record spinning faster than the center. The size of a plate has very little to do with how fast it's subducting or spreading.

More surface area for convection currents in the mantle to push against