This is a blanket statement and completely untrue. Good driving experience is directly correlated to TRACTION, not just weight. And traction isn't just a function of weight - it also is affected by center of gravity, friction between the wheels and the road. Traction is what gives you the perception of being in control of the car.

I used to own two cars of the exact same model - one petrol and one diesel. The petrol is lighter in weight, about 100+ kgs lighter than the diesel variant. And the driving experience on that is slightly scary especially on roads with strong winds. In fact, it is so light that if you drive over tiny puddles or rumbles strips, the car will sway sideways. The diesel always feels more planted because it is front-heavy, thus adding more traction to the front wheels (both are FWDs). I always prefer the diesel for longer drives because of the heft and confidence it provides.