The ready action shows that it is something like pulling the weapon out and readying it for use.
Firing the same weapon twice: Yes, because the weapon is ready and you get two simple actions per round.
Firing two different weapons: Yes, each weapon being fired is a simple action if they are both readied. If they are not both readied then no you can't fire them both at the same time.
As long as the player doesn't exceed 2 Simple Actions they can do it.