On top of the extra scaling, I think there's also the hidden "moveset" modifier value. So a 2-handed R1 attack will have a built-in higher damage than a 1-handed R1 attack, even though they'd have the same AR (for weapons with no scaling, for example). But since these modifiers are hidden, and vary from one weapon to the next and one move to the next, it's hard to pin down a value on them. I know it sounds kind of like a cop-out to say this ("it's a hidden number, don't know its value, but it must be there, it explains everything"!) but I'm pretty sure that's how it works.
I don't know if it varies depending on upgrade level though. I wouldn't think so, but it should be tested, you're right to bring it up. Wouldn't be very hard to test, either. Just compare your 1H and 2H damage, then upgrade the weapon, and compare again. This way you'll see if the increase it the same. I'd do it, but I'm taking a break right now.
I don't know if it varies depending on upgrade level though. I wouldn't think so, but it should be tested, you're right to bring it up. Wouldn't be very hard to test, either. Just compare your 1H and 2H damage, then upgrade the weapon, and compare again. This way you'll see if the increase it the same. I'd do it, but I'm taking a break right now.