The concept of corner weights not mattering on a kart (for which I read, only worry about front/rear weight distribution, not left/right) is nonsense. Moving your body, steering the kart, etc alters the longitudinal weight distribution as much as the lateral weight distribution.
Certainly, getting the front wheel weights to match is less important on a kart than a single seater race car, but aiming to get close (or perhaps, aiming for repeatability in distribution; 50:50 lateral distribution may not be quickest) can be worthwhile if you're going to the lengths of putting your kart on scales in the first place.
Regarding wet driving, whilst tilting your head back may not have a significant affect, shifting a significant proportion of your body weight certainly does. If you agree that seat position makes a difference, you can only agree that moving your body weight in the kart makes a difference.
My own view on the validity of scaling a kart is that, if you're of average enough size and build, sticking the seat where it's comfortable is as good a starting point as any.
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