Washing out the outer span (i.e. decreasing the geometric incidence of the local section) of a swept wing does not directly increase the static stability of the aircraft (see addendum). The analysis mentions flying wing, but is applicable to any swept wing.
1. Stability
Static stability of a low-speed and structurally rigid flying wing is defined by having a negative variation of pitching moment with increasing angle of attack ($C_{m_\alpha}<0$), and is primarily achieved by the planform and the airfoil distribution:
- Planform: the swept outer span offsets the aerodynamic center aft, just like a traditional tail.
- Airfoil: the use of reflex airfoil allows for smaller unstable pitch variation at quarter chord, which further improves stability.
I'm going to skip why a negative pitching moment slope is necessary for static pitch stability, as this has been well discussed here (e.g.). Since the swept portion is (hopefully) aft of the CG, washout acts like a tailplane incidence and plays very little into stability.
2. Trimmability
However, stability is not the only concern. Trimmability is the other (some may argue even more important) issue: at the desired wing lift (or angle of attack), we must ensure that the total pitching moment is zero. This is shown graphically below, where a fully trimmed state is point A:

Image ref: Etkins, Dynamics of Flight
Traditionally this is achieved via pitch surfaces such as tailplane incidence and elevators (by shifting the above $C_m$ curve up and down such that point A can lie at the desired angle of attack). For a flying wing, elevons can be put to use. But it's less effective due to shorter moment arm. If the pitching moment is too negative, we may run out of available elevons to trim or left to maneuver.
Help can come from two sources:
- Airfoil: reflex airfoil generally has positive pitching moment at zero angle of attack. This decreases the overall pitching moment of the wing.
- Washout: since the swept portion is (hopefully) aft of the CG, it effectively acts like a negative incidence on the tailplane, alleviating elevons travel.
With washout, a larger range of forward CG becomes possible due to elevons alleviation. This indirectly helps with stability if the static margin of available CG range had been too small without the proper washout.
3. Addendum
Since washout modifies the lift distribution on the wing, it changes the downwash on the outer span ($\frac{\partial{\epsilon}}{\partial{\alpha}}$), which does affect stability. However, this effect is secondary to what had been mentioned.