I tend to disregard what George says because, to me, it doesn't make sense. But then that gets into philosophical discussions about the nature of the Force and what "balance" actually means.
Personally, I think the "balanced" aspect is one that George DOES allude to in the films, but one which he doesn't quite explain. Basically, the Jedi in the prequels are the emotionless, stuffy eggheady monks. They don't feel, really. They are "mindful" of the force, but they don't FEEL the force. And they're afraid to because indulgence of certain emotions and passions leads people to the Dark Side. Greed, anger, hate, etc.
So, the Jedi tend to forbid themselves from feeling anything that might lead them down that path. Not only that, but they forbid anything that would be a precursor to THAT. So, no love or marriage, for example.
Then along comes Anakin. Anakin is this walking ball of emotions -- turbulent ones too. He's pissed that he's a slave (or was). He's pissed that his mom died. He's frustrated that the Council won't make him a master. He's deathly afraid of losing Padme and will do ANYTHING to save her. He's got no filter on his emotions at all. He doesn't control them. To the contrary, he pretty much just vents them whenever the hell he pleases.
As he grows in power in the force, he uses his emotion to further his abilities, which makes him even more powerful. And ultimately he's more powerful than pretty much all the Jedi because they're all stuck being so repressed that they can't tap into that side of things without going bad (or so they tell themselves).
Anakin, however, sires Luke. And Luke, as I see it, is the real balanced one. Luke feels his passions, he loves his friends (and eventually Mara -- but that's not in the movies). He can be impulsive, but he also is deeply passionate and -- most importantly -- he doesn't deny himself that passion. He contains it, he doesn't just vent it everywhere, and he doesn't let it rule his life, but he does allow it to exist. Something the Jedi were never really able to do in the Old Republic.
So, ultimately, Luke is the one who achieves the balance with the force, in other words, living in harmony within himself and with the universe at large, and without denying essential parts of who he is.
To me, that's the only thing that makes the experience of the force "balanced." Otherwise, I'd have to go with Burton's analysis that it's all about bringing "peace" to the force and Lucas just picked the wrong word.
Although, honestly, in the end it probably isn't even worth all this work. Lucas told us the answer. We just may not agree with it. Balance to the force, according to Lucas, meant killing the Emperor and destroying the Sith. I don't get how that = balance, but whatever. There's a lot I don't get about the Prequels. There's a lot I think George himself probably doesn't quite get about the Prequels.
) say that he "brings balance" when he throws the Emperor down the shaft. There is no baddies left, and the good guys roll. 
