The next levels in the Chrystarium should open up when you defeat certain bosses. I can't remember each one at the moment. Just keep truckin' and you'll eventually get more levels unlocked.
As for upgrading your weapons, when you get to a certain point in the Vile Peaks, you get the option to upgrade your weapons and accessories at save points. You should be close to getting there since you said you were in chapter 4, and I believe that's where the Vile Peaks are.
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