When you first start ng+, your leviathan axe and blades will keep all their previous upgrades which is great since you won't lose that progress. The real interesting stuff happens with those primal flames though, letting you push past level 9 and hit that new level 10 cap. Just remember that certain abilities stay locked to story beats - like when you get the draupnir spear's wind gust move, you'll need to reach that specific part again even with your powered-up gear.

Something worth noting is the timing of your special arrows, since you'll need to unlock those again at specific story points. The key to managing your progression is understanding that while your base weapon power carries over, some of those fancier moves need to be earned again through the story. When you do get into ng+ though, definitely keep an eye out for those primal flames and skap slag materials, since they're essential for pushing your equipment to those new higher caps. Good thing is once you start finding them, you can really feel the difference in combat especially against those tougher ng+ enemies.