"Things You Wouldn't Know If We Didn't Blog Intermittently."
The centre of mass (middle of the slinky) falls down just like any object you'd drop. It's just pulling itself together at the same time, so the ends accelerate towards the middle at the same time, so the bottom hovers and the top actually falls twice the rate of gravity. I'm not sure but it's probably a coincidence that the spring force equals gravity so closely.
Nope, that's not a coincidence. The precise equilibrium is the result of the fact that the situation starts out with the slinky being extended fully; that is, exactly to the point where gravity and spring force cancel each other out. This is independent of the absolute values of either force, as can be seen from the second, rainbow-colored slinky in the video: Its spring force is doubtlessly different from that of the first, but nevertheless the behavior is exactly the same. A lot of information on the process can be found here.