Stiffer springs, as well as sway bars, help keep the car from rolling side to side as much, which means there's less weight transfer while cornering. The center of gravity doesn't move as much, plus it helps keep more weight on the inside tires in a corner, enabling them to participate more in the quest for traction.
My guess is with a passenger in the car, the ballast is helping the car stay lower and possibly even leaning less in the corners. Stiffer springs will do the same thing, but you need to also address ride height at the same time; stiffer and taller may work in some activities
, but not necessarily car handling. The ultimate objective would be to keep the CofG as low as possible, while minimizing side to side weight transfer, while still keeping all 4 tires in contact with the pavement. Yeah...you do see the occasional vehicle that corners on 3 wheels, but if done right, its counteract other deficiencies in the handling design while achieving a better blend of traction and handling.
IMHO, the best compromise for street & track is stiffer sway bars to help control the side to side leaning, while still enabling the springs to provides some bounce and compliance when driving on the street. FWIW, softer springs are also a benefit in the wet, because it helps keep the tires planted to the street surface over bumps and such. Of course, if you were drive the track in the wet sometime, you would better understand.
Regarding Steve's recommendation to stiffen springs on one side, that's simply his way of slowing down the competition. Corner balancing the car, with you in the driver's seat, would provide a more pleasant outcome.
.....unless you possibly have NASCAR ambitions.