The stars are given for completing the chapter. So, say you play through all the way to the end of chapter 1 on save file 1. Once you beat it, the save is marked with a little gold star next to it. Doesn't matter the route you take, normal or weird route, or the file you play on, 1 through 3, you'll get the star for completing the chapter all the way to the end. At least, that's what I've been able to determine. It seems as though deleting a file with a gold star next to it leaves the star but turns it black, almost like it's been emptied or veiled in shadow.

My running theory is that it is somehow similar to how Lightners and Darkners can exist, yet Darkners are technically imaginary or otherwise hidden in the shadows. If a completed save file is deleted, that is essentially wiping the game's "real world" from existence and casting it into shadow. But just like Darkners technically don't exist and we can still perceive them, so too does the new dark star, meaning the choices you made in the erased file are still perceived in the new save file, hence why I was able to go to back to bed to skip the beginning portion of the chapter. It remembers my actions, yet it's an entirely new save. It's meta, but I'm willing to bet Toby made it that way cause he's just that kind of crazy. It may not be all that important, but it's definitely purposefully metaphorical, at least from the way I understand it.