Lighter cars are typically safer than heavier cars (as is indicated by your link).
I screwed up with that source and deserved the moderation down, but this isn't true either. Heavier cars are safer for the person driving them. The direction US cars have gone is based on things like this 1997 weight study, where the conclusion was that passenger cars would be better with an extra 100 pounds.
However, having a fleet of heavy cars around is more dangerous for the average person, which is what the EU statistics show, and that study points it out too. At the same time as showing cars would be better if heavier, the study also shows making light truckers lighter would be good. The important point in their words, and I'll bold it because it's the most important thing here: "When trucks are reduced in weight and size, they become less crashworthy for their own occupants, but they become less capable of damaging other vehicles."
If everyone has a light car, the average accident isn't as bad as two heavy cars colliding. That's Europe right now. Average car is heavier but you're also in a heavy car, that's the American roads. Worse overall, but it's not as bad if you are in one of the heavy cars! The really bad case is when you're driving a light car and you hit a heavy one. That's what I was describing with the EU car on I-95 example. The end result is a sort of arms race in American car design. Everyone has a a personal incentive to drive something heavier for their own safety, but everyone would be safer if, collectively, we didn't do that.
Another reason the busy American highways are dangerous is all of the trucking used to move things around. My personal distaste for being in a light car here in the US comes from watching a few car -> tractor-trailer accidents back when I used to drive quite a lot here. Whenever I'm in something like a London taxi, worrying about a collision with a truck in that tiny vehicle makes me crazy. I have to remind myself that the road isn't filled with those big trucks though, and overall that's an improvement.