How does wing sweep increase aircraft stability?
Directional stability

When a swept wing is flying in a sideslip, the windward side behaves like a wing with less effective sweep $\varphi_{eff}$ and the leeward side like one with more effective sweep. Wing sweep  causes a flattening of the lift curve slope for two reasons:


The effective angle of attack is reduced by the cosine of the sweep angle.
Only the component of speed normal to the quarter-chord line of the wing is creating lift, so a swept wing creates less lift per area than a straight wing.




The increased lift rolls the aircraft, but also produces increased lift-induced drag which pulls it back to straight flight. The sketch above shows this for the flying wing glider SB-13. This effect is so strong that swept, high-wing configurations need anhedral to keep the sideslip-induced rolling moment down.

For completeness, also the side force $Y$ of fuselage and winglets is added and shows that the winglets help a lot to create directional stability. This is needed in case of the SB-13 because it has a nearly elliptical lift distribution. Using a triangular distribution (N9-M) or even a bell-shaped distribution (Horten flying wings) avoids the need for winglets, but causes higher induced drag in straight flight. Another downside is a low directional stability at high speed, because this sweep effect increases with the lift coefficient on the outer wing.

Longitudinal stability

Wing sweep also helps in longitudinal stability by stretching out the wing lengthwise. This is important for flying wings which lack a separate tail surface. By changing flap angles at the center or the wing tips, the lift at the most forward or most backward sections can be changed for pitch control, and more sweep increases the lever arm of these changes. Also, in swept flying wings natural static stability can be achieved without the use of reflex airfoils, but by applying washout. Again, the higher the sweep angle, the less washout is required.

Too much sweep?

Easily! Sweeping a wing creates lots of problems:


Sweep reduces the lift curve slope and the maximum lift of a wing. The maximum landing attitude with a highly swept, slender wing is severely limited by wing tip clearance, so swept wings need powerful high-lift devices.
Sweep causes the boundary layer to be washed outboard, which will cause nasty stall behavior once a specific ratio of wing aspect ratio and sweep has been exceeded. This can be somewhat limited by wing fences, but should better be avoided altogether.
Sweep changes mean that bending moments will partially get converted to torsion moments, requiring a torsional stiffening of the wing.
For flying wings, sweep will let the aircraft center pitch up and down when the wing flexes. This creates a powerful interaction between the fast period mode (which is only moderately damped in flying wings) with the wing bending mode, resulting in flutter.


Why sweep a wing at all?

Generally, an aircraft designer will allow only as much sweep as necessary. 
Wing sweep reduces drag when the aircraft flies with transonic or supersonic speed. Now the Mach effects depend only on the normal speed component, so they are proportional to the cosine of the sweep angle. For the N9-M this was not a factor, however, the B-2 benefits from it with a higher drag divergence Mach number.