I'm currently running my first D&D 5e campaign. Everybody at the table is new to the game as well, so nobody can really answer the question. While preparing for the game I was reading through the weapons section and came across the list of weapons in the PHB which state the damage for each weapon. A question came to my mind:
Let's say I have a barbarian in my group wielding a greateaxe with 1d12 + Str mod damage when starting the campaign. During the campaign he (or she) come across an old and legendary forge and a smith who offers to strengthen the greataxe due to the enormous deeds the group has done. The smith takes the greataxe and imbues it with obsidian shards (or whatever): does the weapon then get better stats?
As far as I understand it would probably be up to me (the DM) to decide on that, so I could simply rule that because of the treatment the weapon got when it was created it deals 2d8 + Str mod damage from that point on.
If I rule this way, how can I be sure that the weapon doesn't get overpowered in comparison to the weapons enemies have?. Same thing holds for looted items.
Let's again say we have the barbarian with his 1d12 greataxe but he finds another, way more beautifully built one than his own. The weapon looks as if the metal was really well crafted (etc. etc.) so the weapon is really a better crafted version of the greataxe that he has.
According to the rules this would still be a 1d12 weapon, but for me that would have some strange taste to it. They could start asking themselves, why they should loot any found weapon if it doesn't benefit them at all.
I know that they could have magical effects to them (as stated in the Magical Item sections in the DMG) but that's not the situation I'm talking about. I'm talking about the same (or equal, I mean a really well crafted sword could still be better than a badly crafted greataxe) weapon (non-magical), just a way "cooler" one.