I think this is the proof JerseyTom asked for (you know my mantra: "don't give me opinions, give me numbers").
If I assume that the CG is at 1 feet of height, the wheels are 7 feet apart and the load is the 7000 pounds someone assumed, then, when the car is going in a straight, we have this:
If the car takes a curve at 1G, then we have this:
The torque around the CG is equalized (as you all know) by a lateral weight transfer, like this:
Thus:
Then, the left wheel (I'm assuming we're looking the car from the front) "weighs" 4.500 pounds and the right wheel (to the left in the image) "weighs" 2.500 pounds.
Now, if we increase, let's say, 0.1 feet (that's 3 cm, give or take) the front width, we get:
Thus:
That's around 30 pounds of difference. So, we get the 30 pounds "asked" when the change in width is 3 cm, not 1 mm.
Anyway, I don't think that 30 pounds is going to make any difference at all in the feeling: it's like 0.5% of the weight...
Now,
if this change in weight of 0.5% "translated directly" in laps 0.5% faster, this would mean that for a 1:30 lap you'd get a difference of 4 or 5 tenths (I don't think this is the case, but...).
Is this the case?
However, if we move
just the left wheel 0.01 of a foot (that's like 3 mm) I find a change in force of 7 pounds... which is around a fourth of the change "required".
Same goes for Center of Gravity height: a change of 0.01 foot equals 10 pounds.
So, a change of 1 mm in width is no big deal, as JerseyTom correctly states. A change in the position
of one of the wheels could be felt at half the distance "required". A change of 1 cm in the CG height gives you 30 pounds more weight on the external tyre. Perhaps that's why Alonso has lost weight...
Conclusion: when you race, check the "width" of both tyres. The distance of both tyres to the CG must be equal to the centimeter or less, or you are changing the attitude of your car in a significant amount, even for small movements of the tyres.