You can level up Blade, Blunt, and Hand-to-Hand at Peryite's Shrine east of Bravil. There are a bunch of robed figures there that don't respond to damage at all, making them the perfect punching bags.

Leveling up weapons in The First Descendant can be done at the repair station workbench you can see above. However, you'll also need to find Anais, the magister in charge of research to make a ...