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.