If you really could dig a hole to China, and you did, and you fell in, would you stop in the middle because of gravity?

Assuming that you did dig through the center of the Earth, yes.

You'd melt, and probably evaporate, and heat rises, so.... :S

Plus the magma in the mantle would rise, cool down to a solid, expand, and you'd just land on very hot lava.

There's a center of the Earth?
I thought it was an alien spaceship.

#doctorwhoreferencesareawesome

Yeah, you would. I read this awesome book called "Tunnels" in one of the later, they are at or near the center of the Earth and they are weightless. i asked my Dad about it, and he said that yeah, you really would be weightless because the mass of the Earth is pulling you in every direction.