I can't imagine the weight distribution changing in any noticeable way at all. The difference between running with half a tank of gas vs a full tank would be much greater. If you can't tell the difference in handling after you fill up, you'd never notice this. The center of gravity of the caliper isn't even moving the entire diameter of the rotor, you might be moving the caliper all of 8". Might not even be that far.
As far as other advantages, the biggest one that I can think of is clearance for the front sway bar on the pre-'73 cars, the '73+ calipers tend to interfere with the end links. But that's only if you keep the pre-'73 K member and sway bar.