It varies depending on what i'm doing. When just stepping I'd say it's pretty low, knees to dantien, but in contact, depending on the forces involved, it fluctuates around the dantien, sometimes above, sometimes below, though less so.
as for why? Lower is better, IMO. I pretty much want to feel like this thing would if you were grappling with it:
the result? stability, but people are also easier to move, but that's not just a result of that alone. As I mentioned above, it fluctuates depending on the level of force we're talking about. In most aikido waza I think it's fairly easy to maintain and keep low because there isn't as much force involved, but if I want someone to feel the difference I'll do it from a clinch position or simple pushing. It's pretty easy to clinch up with someone and have them push you around, try to move you and let them feel the difference, but again, it's force dependent for me.
IMO it's all a product of focused relaxation and you cannot just will your body to relax against forces that are greater than what it's been conditioned against any more than you can go from curling 20lbs to curling 100lbs without building your way up. If you try, all the various muscles you're trying to avoid using will start to kick in and your weight will travel up to meet it.