I'll go out on a seriously precarious limb here and say (having looked at a picture of the innards of an ASI, sorry I can't reproduce it here easily), that:
1. Assuming that the centre of the capsule (which pushes a horizontal lever) extends with the square of the speed, then
2. That extension, which is turned into a rotational movement of a vertical rod, has less effect the further the capsule extends, because of the rotation of the vertical rod. That is, the first mm turns the vertical rod say 2 degrees; the next mm turns it 1 degree and so on (a bit like a piston in its travel - at top and bottom dead centre the crankshaft rotates heaps but the piston doesn't move much, whereas halfway between those two points the piston moves fast for a small rotation of the crankshaft.) It's a sine curve kind of thing.
Ready to be shot down any minute now!