Superweapons. They're a staple of Star Wars. Sure, they were over used in the early books, novels and comics, but they also provided a highly defined and specific target and goal for the story. Eventually, the stories moved beyond the superweapon of the week into other topics, but....
Have you used a superweapon in your Star Wars RPG game?
OK, so if you played Dawn of Defiance, there was kind of a superweapon in that series, but it was more of proto-superweapon and more of a distant threat, rather than an immediate one.
So, why not?
Stats? Sure, we didn't stat out the big bad superweapons. But they're generally one-shot = one kill (planet, star, whatever). You don't exactly need hit points for this sort of thing.
Silly? Possibly, but I bet if you take it seriously, and avoid a supercheesy weapon name, you're players will likely buy in.
CL? It's more of a dramatic device. Try not to over think it.
Overwhelming odds? Goes with the super weapon territory.
Dubious plausibly? Very likely. Roll with it.
Ideas? Well, there are the old sci-fi, pulp story plot devices, you can start with a couple of those and mix and match as you like.
Massive weapon + transportation device + power source +evil villain + evil sidekick + underlings = superweapon
Weird alien/person/creature + primitive tech (or) super high tech + captured/crashed/stranded heroes = unexpected help
Previously unknown world, city, star, asteroid, etc. covered in suspiciously red cloud formations or rocky red soil = superweapon target
Serously, though, superweapons are actually underutilized resource in most Star Wars RPG campaigns. It doesn't have to be on the scale of the Death Star, and it really shouldn't be. However, there are plenty of weapons ideas for RELATIVELY smaller targets that can be equally threatening for the scale of adventure they're used in. Some of the vaguely referenced novels and comics can give you a starting point. Didn't like a particular superweapon? Improve it yourself and see how you players react in game.