I can imagine a few ways that increased mass in the car would help handling.
As mentioned earlier by Marvin, the centre of gravity can be manipulated and moved closer to the ground, which can help keep all four wheels more evenly loaded when under acceleration either laterally or forward/back. The forces acting on the car to accelerate it (friction between the wheels and the track) are on the ground, and the closer the c of g is to the ground, the less of a torque is induced to roll the car (either sideways or into a wheelie/endo).
Also, mass generally increases the inertia of the whole car, so it is more stable and "unwilling" to be accelerated in weird directions by bumps etc.
I suppose you can also manipulate the polar moment of inertia a bit - that is how "centred" the mass is in the car. If the polar moment is reduced, (mass in the middle) the car will change direction more easily than it would do if the mass was at the ends of the car. Think of how it's easier to spin a 500g mini-football than a 500g hula hoop...
Further, it improves the unsprung mass ratio so the suspension works better. That is the fraction of the car's mass that is not "suspended" by the suspension (e.g. wheels, tyres, and a fraction of the suspension parts) is lower. Think Hornet!
But hey, I'm certainly not a top-flite driver, but I've got a pretty good head for these general concepts. I'm totally willing to be corrected though!
Cheers,
Ty