The Stray Cats are primarily a rockabilly band...
Double basses are typically hollow. Most standard 3/4 wooden double basses weigh between 20 and 25 pounds. A good carved classical (or orchestral) bass is probably going to be on the lighter end of the scale, a rockabilly plywood bass -- which is more likely to be stood on and tossed around -- will be heavier. Costs also vary similarly, a very nice classical bass could cost ~$200K or more, a good rockabilly bass probably under ~$10K. My 1930s aluminum bass, which is setup for a variety of music including rockabilly, weighs 28 pounds fully setup; I don't stand on it or toss it around though.....
The showmanship factor is high and obvious with rockabilly and those basses can get abused, so dedicated rockabilly basses can be built for rough treatment and they are typically optimized for amplified tone and volume. On the opposite end of the spectrum, showmanship is present but much more subtle with classical basses, they are built for acoustic tone and volume, and other than in some school environments, these basses are typically treated in a way that is respectful of their value.
I'm no expert at either of these musical environments, so hopefully we'll also hear from some people who do specialize in them.