You can take equipment to an upgrade shop to strengthen them, improving their properties and also adding special skills once they're upgraded enough. Through fortification, weapons could end up changing into different weapon types.
During the normal gamplay you'll only be able to upgrade weapons to level 9+ or less (5+ is more common). Instead, you'll be able to upgrade armors up to level 9+, with exception of the special ones (Calista's Ballgown, Calista's Dress and Knight's Attire). However when playing New Game Plus mode you'll be able to upgrade every weapon up to level 99+ (with exception of the crossbows) and some armors even up to level 32+.
There are some armors in the game that can only be upgraded at a certain shop. These are: