Why did the DC-3 have wing sweep?
The wing was swept to move the center of lift back, closer to the center of gravity. When the design of the DC-1 was advanced to a point where the center of gravity became clear, a redesign of the wing-fuselage intersection would had been more effort, so the outer wing panels were swept back a little.

From this website by Jeff Lucker:


  the unique and characteristic swept wing of the DC-3 was an attempt to
  keep the wing in its original location as the center of gravity moved
  toward the rear.


When Douglas produced new variants (DC-2 and DC-2 sleeper, a.k.a. DC-3), they kept the proven layout.