heavy exersise ball (not weighted but can stand on it) is should't be pumped all the way the less air easyer to stand on. use a frined to stand on it or put it inback or side of couch but dont let ball tuch it.
work on standing on the ball for a while then slowly work in squats then when u master than u can incorperate weights. its surfing training for balance in big waves. i saw laird hamilton doing this on fit.tv and been working on it (im doing no weighted squates now with a almost fully pumped ball)
when i wrestle back yard style video jiu jitsu (bought ceaser gracie video =) ) i found my stand up take down defense is better my legs are alot more strong and are harder to manipulate. they are used to the shakes and wabbles
Sounds to me like you need a course in footwork. Find a boxing coach, or a good reference book, and an open are to drill footwork. I find that footwork is grossly undertrained by many MMA guys, which is a shame, because good footwork would make the stand-up portion for a lot of guys much better.
Also, and this may seem odd, go out an start dancing. If you want to find a real good way to sharpen your sense of balance while working out in a trying cardio-stressing environment, dancing will do wonders.
What works really well is a fit disk. Its a rubber disk about 14 inches wide and about 2 inches thick that you fill with air so you can control how much stability it provides. First practice standing on it with both feet, keeping an erect posture - this will be quite difficult to start but you will rapidly improve.
Then move on to standing with one foot - the disk should be firm enough so that you do not touch the ground through the disk but soft enough so that it doesn't provide much stability. Then practice standing on one foot and moving the other leg around in a circular motion - this will change your center of gravity and will require the small muscles in your ankle and knee joints to develop and become stronger which will drastically improve your balance. Once this becomes easy try squats with two feet on the disk and then single leg squats.
From there you can do all different types of exercises while making sure you keep an erect posture and your balance. Just use your imagination.
This will dramatically increase your balance and also your focus which is just as important. Make sure that you keep your attention focused straight ahead - do not look down at your feet while you perform the exercises. BTW a fit disk is cheap - you can pick one up for about $20 at any good fitness store. Forza is a good brand.
Another good piece of equipment is a wobble board made by Fitterfirst which is a bit more expensive - approx $50. However, it has a hard surface and is not as efficient at developing the small muscles in your joints which are critical for balance.