The bigger=safer concept isn't really true. If all else were equal, you'd be safer in a bigger, heavier car. But all else isn't anywhere close to equal: not just design, but driver attitude as well.
The IIHS listed driver death rates by model in its status report Vol 40 No 3 at http://www.iihs.org/sr/2005.html. For example, the 4-door Civic had 67 driver deaths per million ownership years, the Excursion had 107.
Note that the IIHS itself really likes big vehicles. Most of the text of the report talks about safety increasing with size, even though they vary widely within the groups. They pushed hard for the recent CAFE changes that lowers mileage targets based on size. But it's pretty clear that design and driving has a huge influence on safety.
On the Corolla, I remember they had so-so mileage until the 98 switch to the ZZ engine. The old cast-iron engines were seriously reliable though.
I've noticed a decades long trend for autos to creep upward in size. It's part of the effort to increase model loyalty. They eventually get large enough that they either downsize in a large leap or bring in a Yaris or something.
Reality is merely an illusion, albeit a very persistent one. - Albert Einstein