It was difficult to find specific information about this, especially as it would seem to be a widespread Mavericks problem. I posted here because I initially thought the problem might have to do with Creative Cloud's authentication process.
It turns out that Dreamweaver CC has some Java SE 6 runtime dependencies, but Mavericks comes with Java 7. I'm not sure why this hasn't been remedied by Adobe by now. Apparently some Mavericks users had been prompted by DW upon launch to install Java 6—which could explain why the problem hasn't shown up more on the forums as it was quickly remedied—but my copy never got that far. I did have some trouble tracking down where to download Java 6 for Mac, as it's not on Oracle's site, but found it here: http://support.apple.com/kb/DL1572?viewlocale=en_US&locale=en_US
After uninstalling DW (again!) and installing Java 6, I re-installed DW and it opened.
The other suggestions about given had to do with older CS6 apps not working and weren't helpful to my specific problem.
I'm posting this in case any other user has experienced the same problem in the same way.