This is taken from a scooter forum;
First things first, this info assumes you know how a CVT works.
The job of the contra spring is to maintain appropriate tension on the drive belt, raise the belt up the rear pulley during deceleration, and balance the force of the roller weights to maintain the RPM range in which the gear ratio of the CVT varies. Here's how: When torque is applied to the front pulley, the roller weights cause the belt to rise, increasing the gear ratio of the pulley. Since the belt is a fixed length, the reciprocal action is that the belt must be pulled down towards the center of the rear pulley, raising the gear ratio simultaneously in the rear. The contra spring resists this force, creating a balance at a certain RPM range. Why is this important? The roller weights can't be too light or too heavy in relation to the stiffness of the contra spring. If you go too light on the weights, top speed will suffer. If you go too heavy on the weights, acceleration will suffer.
The contra spring also helps climb hills. As previously explained, torque from the front pulley raises the gear ratio and compresses the contra spring when accelerating. The reciprocal action happens when you climb a hill. Resistance is applied to the rear wheel, the bike slows down, and the contra spring pushes the belt back up the rear pulley until it reaches a ratio that provides enough torque at the rear wheel to climb the hill at that RPM. The engine RPM's change relatively little as the scooter slows down because as the gear ratio decreases, the scooter will travel slower at the same engine speed. If your RPM's drop dramatically and your engine starts lugging, you need a stiffer contra spring.
Here's a YouTube video of a weak contra spring demonstration...
Contra springs also put you in a lower gear ratio when you roll off the throttle or hit the brakes. The variator is doing the same thing as when you climb hills, only caused by change in throttle input and/or braking rather than change of slope of the road. The "coasting" effect upon roll off comes from the fact that the pulleys are still being turned during deceleration, even though it's from rolling along. This limits how fast the contra spring drops the gear ratio back down. I suspect the reason stiffer contra springs are billed as "performance" items is because the added resistance increases RPM's and theoretically would inherently decrease any lag time in sudden downshifting... say from riding very fast in a high gear ratio, slowing suddenly for a corner, then needing to accelerate hard back out of it. I image the trade off, after a certain point, would be excessive heat/friction losses, belt wear, and limited top speed.