Just like an Armor Smithbox, a Weapon Smithbox will allow you to reinforce your weapons at a Bonfire. You can only upgrade to an ascension point, either +5 or +10. To step over these points you will need to visit the correct Blacksmith.
Andre of Astora will sell you either Smithbox for 2,000 Souls and you will need one for each play through as they are removed after the final battle.
Not to be confused with the Repairbox, which will only repair wear and tear damage (Durability). The Repairbox is also sold by Andre.
Andre of Astora, the Blacksmith. Happy to take your Souls in return for some chat and a good job on your hardware.