Double weapon XP tokens DO stack in #Warzone.

Can you stack weapon XP?

It's also important to keep in mind that while you can't stack Double XP, the game will still allow you to consume them. There is an in-game warning, but you still want to be careful and make sure you're paying attention.

Does Double XP count for weapons modern warfare?

After searching more, it sounds like you can unlock things specific to weapons such as attachments, etc with "Double Weapon XP", but it doesn't help your overall XP. Similarly "Double XP" helps your overall XP, but not weapon-specific XP. Don't worry about answering your own question, that is fine.