Well there are skill proficiencies using a skill on a weapon over an over eventually makes the skill stronger, and after you pick up Momotarou you can evolve the skills on weapons but im not really sure how that works.
the only way to make the weapon itself stronger is to reinforce it by scraping other weapons to make it stronger, once it reaches a reinforcement limit of +10 you can smelt it using another weapon that shares your weapons name to increase the reinforcement limit another 10