The laws of physics say that handling and braking should be independent of weight.
Frictional force = coefficient of friction * ( mass * g + aero downforce )
Centripetal force = mass * v^2 / r
When cornering, these must be equal, so the mass terms cancel out in the absence of aero downforce and we have:
g * coefficient of friction = v^2 / r
i.e. the speed at which you can turn around a given radius depends solely on the coefficient of friction (and the gravitational constant, but that varies only a relatively small amount over the planet, and isn’t something that can be altered by tuning the car).
A similar argument applies to braking.
If you have aero downforce, then that increases the frictional force without increasing the centripetal force, and hence allows faster cornering and reduced stopping distance.
A related issue is that wider tyres shouldn’t increase grip, as the frictional force equation doesn’t depend on contact area. As wider tyres don’t change any of the terms in the equation, frictional force should remain constant. I’ve actually rationalised that one by pretending that when you make the tyres wider, the game is silently using a softer compound, i.e. the compound for “race tyres” in size 245 is a softer compound than the same tyre in 225, for example. As far as I’m aware, this has some basis in reality as explained here:
“Soft compound tires are required to be wider in order for the side-wall to support the weight of the car. Softer tires have a larger coefficient of friction, therefore better traction.”
So I’ll leave the tyres, but I’m struggling to rationalise the effect of weight in the game.
Maybe we could see it as accounting for tyre wear even though the game doesn’t explicitly model tyre wear? A heavier vehicle will wear out the tyres faster due to the increased force at the tyre-road interface, so if you have a finite tyre life for the race, you’ll have to corner more slowly to make them last the race if the vehicle is heavier. So we could perhaps look at it that way, that reducing weight giving better handling and braking isn’t a direct effect, but rather the game enforces equal tyre wear over the race duration and therefore the heavier vehicle must be given inferior braking and cornering ability to achieve it?