It's a combination of NVH, safety, and convenience.
Light cars tend to feel kinda thrashy unless the suspension is quite soft which leads to the car feeling like a boat. Not very sporty. And someone who purchases such a car wants a solid feel with firm handling...so they add weight to take some of the NVH out. This weight is usually in dampening materials, carpets, and even weights bolted onto some parts of the car (like Camaro calipers).
The safety part is kinda easy to visualize. A big car hitting a smaller car will always win. In addition, the more steel you can get between the occupants and whatever object; the better. It's why you see the shoulders on new cars so high; side impact protection. In addition, there's all sorts of support beams in the doors and pillars for rollover protection. Toss in a baker's dozen worth of airbags and the wiring/sensors to go along with them and you've added another Rosie O'Donnel worth of mass to the vehicle.
As far as convenience goes; it's really all the 'extras' like motorized side mirrors, headlight washers, back up cameras, premium sound systems, etc. that people like on their cars. While these 'extras' don't weight a lot my themselves, it's a classic case of gathering all the spit in the ocean to make a small lake. It all adds up.
Lastly, cars today are HUGE! I had an older VW Passat Wagon and it was the same length as a 2dr GTI MkV. It was narrower, shorter, and had an extra set of doors...yet it had nearly the same footprint. My guess, it was lighter too.