Upgrading your weapon is an essential part of Elden Ring. It improves their base damage and attribute scaling, both invaluable when going up against stronger foes. Just be careful with Arcane scaling as it may be broken. In the early-game, you'll find an abundance of regular smithing stones, especially if you go spelunking in the many mines littered around The Lands Between. On the other hand, the early game has few Somber smithing stones - the material needed to upgrade unique weapons. Their initial rarity may make you quickly give up on these unique weapons in favour of the regular ones that are easier to upgrade, but don't be so quick to do that. Dark Souls 3 modder Renjingles has outlined their thoughts on Elden Ring in a Twitter thread, and within that they reveal how much it costs to buy enough smithing stones to fully upgrade both normal and Somber weapons.
As you can read in the tweet above, Sombre weapons only need to be upgraded to +9, rather than the staggering +24 regular weapons need to be buffed to. Also, the cost for acquiring the raw materials necessary to do this is around one fifth the price for Somber weapons.
But how do you simply buy Somber and regular smithing stones? Delving into mines to kill the bosses at the end will sometimes award you with special Bell Bearings you can give to the merchant twins in the Roundtable Hold. These will unlock various levels of smithing stones for sale.
Better yet, while the amount of smithing stones you need to upgrade regular weapons keeps going up each level, Somber weapons only need one stone per level.
So, keep hold of that Bloodhound Fang or the Sword of Night and Flame. They may be thought to upgrade at first. But they'll stay ahead of the curve damage-wise and save you a lot of money and hunting in the long run.