The sun isn't wet. It's not going to dry out.
Strictly speaking asking the weight of an astronomical body is nonsensical. Weight is a measure of force and only has meaning in relation to mass and acceleration (in this case due to gravity). The sun has a mass of 1,988,400×10^24kg.
As to the question about turning it into a rock, let me put it to you this way, "Which weighs more, a pound of rocks or a pound of feathers?"
Or think of it this way. I weigh about 200 pounds on the earth (pounds being a unit of force, not mass). That's the force holding me down on the planet. That's also how much the Earth weighs on me. My mass, about 91 kg, is the same on earth, the moon, outer space, the surface of the sun, etc. My weight however, depends entirely on whatever massive gravity well I happen to be standing on.
Don't ask "What is mass?", there be dragons. You'll either get trite over simplified to the point of being meaningless answers (like the reply below), you'll just barely start to understand that learn more about the world around us leads to more questions than answers. That's kind of the whole point though.
Actually, I kind of hate omelettes. Not that there's anything wrong with them, just not my thing. I appreciate the links though, I might try them. For me it's more like there are things I love without a adding a bunch of other competing flavors to like chocolate, bacon, coffee, a good glazed donut, and eggs.
My scrambled egg recipe can be wet, or drier if you let them cook a little longer. If not for the consistency of the whites, I'd probably prefer my eggs almost completely raw. I like the method I posted because it brings so much of that yolk flavor I love to the forefront with grossing out someone that likes their eggs completely cooked.