No official word on this yet, but you can bet it will be more than 2.
Chances are the game will feature a split inventory system (which is common in RPGs, but might be new to those coming to the game from a shooter background). In a split system you can carry a certain amount of equipment (guns, grenades, and other items) on your character and you can store the rest at some sort of terminal/safehouse/locker . Your storage capacity will be much greater at your terminal/safehouse/locker of course, think along the lines of 50 slots on your character and 500 in the "locker".
I doubt they will go very in depth with the storage system, so you won't have to worry about weight or size of guns/items.
Weight and size is definetely not goin to be a Problem.
The Characters use what Gearbox likes to call a 'Storage Deck' this is practically, just a Digitizer (comparable to the Digitizing in 'Tron' or similar) Weapons and other stuff will just be digitally stored, like on an I-Pod. As far as i know you can carry 4 Guns for direct use and the rest goes to the Deck.
You have the storage deck that basically reads the DNA of the gun and keeps that instead of the gun itself, so you can use it whenever, but the storage deck can only hold a certain number of guns, which can be upgraded by finding Claptraps, apparently.