That's what I'm not sure about: maybe the weapon develops instantly, and time is a "countdown" until the next use?
One sword, crafted on Wednesday and left in the furnace for 2 weeks. I played over the weekend, and the sword was level 4. So, the weapon doesn't develop instantly.
Added 1 minute ago
You can buy 3 more weapons, get one for completing a bonus mission, and two more are available as a pre-order bonus. I'm not sure about the last one: maybe the pre-order actually gives you three weapons, and it's just impossible to get only two?
Can you buy them at the altar? I forgot about that. And is the bonus mission given for a different edition?