Question: The scenario: a level 11+ Fighter has the Feats:

* Two-Weapon Fighting
* Improved Two-Weapon Fighting
* Greater Two-Weapon Fighting
* Quick Draw
* Point Blank Shot
* Precise Shot
* Rapid Shot

How many weapons do they need in a Blinkback belt to perform his full 7 (Main, Iterative -5, Iterative -10, Rapid, TWF, ITWF, GTWF) attacks during a Full Attack?

* 1, because it returns to the belt, so it could be drawn with either hand?
* 2, because each hand needs a weapon at the start of the action?
* 4, because you can't draw them immediately for some reason?
* You can't, because you can't reuse the same weapon, you'd be capped at 4 swings plus other weapons you don't have on the belt?
* Or some reasoning I didn't even think of? Rule quotes appreciated.

Answer: 
The correct answer is 2.

The Two Weapon Fighting feat explicitly requires you to use two weapons to gain the additional offhand attack (italics mine):

> 
> **Benefit:** Your penalties on attack rolls for fighting with two weapons are reduced. The penalty for your primary hand lessens by 2 and the one for your off hand lessens by 6.
> 
> 
> **Normal:** *If you wield a second weapon in your off hand*, you can get one extra attack per round with that weapon.
> 
> 
> 

For the same reason that you can't use a single weapon between your main and off hands while using TWF normally, you cannot do this while throwing weapons.

The Blinkback belt teleports the weapon back to the belt immediately after the attack is resolved, so you won't need more weapons than the two needed to satisfy TWF.
As spec'd out, the fighter could have all 4 light weapons on the belt and would still be limited to 2 attacks: the blinkback effect only happens when the "wearer draws a weapon attached to this belt and throws it before the end of her next turn" after which the weapon returns "to its strap or sheath", which necessitates drawing the weapon again.

Drawing a weapon is a move action. Even though the fighter can draw a light weapon in each hand at the same time (with Two Weapon Fighting), they'd still only be able to draw two weapons (during their move action) and make two ranged attacks (during their standard action, with the resulting Two Weapon Fighting penalties on the primary attacks).

If they also had Quick Draw, two weapons would suffice - drawing then becomes a free action, so the fighter could draw weapons sufficiently quickly for all of their attacks to go off, and they could always draw both weapons to start their next (iterative) two-weapon attack.