I noticed that I could sell armour to some vendors, but I was pretty sure that not all people will accept clothes and I was wondering if there are any vendors that will buy weapons?
According to this source, it is not possible to sell weapons:
Nope. Weapons in the game looks likes a completely different kind of item. There's abundance, but you can't trade, repair (usually) or buy them. They're spoils.
The exception appears to be armor only.
The NPC who gives you the side quest to get a piece of Royal Guard's equipment will also trade one gem for each piece of Royal Guard's gear you bring her. There's no way to sell regular weapons, though.