I am getting tired of using the old weapon set, and I'm hoping that I can earn new weapons during the career or training modes.
To unlock new weapons, you either have to level up your characters, win at the slot machine, or get them in a [?] box. You'll get most through the slot machine though.
First of all, every ten levels that you advance with your character, you'll get a reward. Most of these are character parts, but most characters give you a weapon when you hit level 30, 50, and 70. The rewards are pre-defined, but it's not the only way that you can unlock these weapons. You can find a list of those here.
You've probably noticed that every game you play you get credits, especially for doing well. Training mode gives you some depending on your rank, and campaign mode give you credits for picking up [?] boxes. The two best ways to get these are to play level 3-3 and to win online matches. Then, you go to your page, then to your character customization, then to the screen that lets you select your weapons or abilities, and then you push the triangle button. (I don't know what it would be on the 360 or PC.) After you get to the slot machine screen, spin a bunch, and you should get a good number of weapons. If you spin all the standard weapons, you'll unlock another tier that costs ten times as much. It's all weapons, and those weapons are really good.
Finally, when you pick up a [?] box, you'll sometimes just get a weapon(or ability or name) instead of credits. It's roughly the same type of weapons that you get from spinning, and it's really rare to get one like this, though.