Aikido folks eventually get the sliding movement as a "sinking" over time. But in the beginning, folks tend to push from the rear foot. Any pushing from the rear foot to make a step raises the center a little bit. Think of a rear wheel drive auto. The front wants to rise when it accelerates.
Now think of a front wheel drive auto. The mass sinks rather than raises.
Yes they may eventually. In the beginning folks tend to do many things.
If you look up the following on google I'm sure you will find it interesting: Koshi balancing-a method.