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Why did the Sunderland end up with swept wings?

Short answer

Because of a balance adjustment. When the planned defensive armament changed — the 37 mm COW nose gun gave way to turrets with 0.303 machine guns — the centre of gravity shifted, and after the initial tests a spacer gave the wing 4° 15' of sweep to shift the centre of lift.

Why did the Sunderland end up with swept wings?
Short Sunderland by Tower BridgeAndrewRT on behalf of Wing Cmdr (retd) Derek Martin (CC BY SA), vía commons

A flying boat born from R.2/33

In November 1933 the British Air Ministry issued specification R.2/33, calling for the development of a new-generation, long-range, general-purpose flying boat. To meet that requirement for a general reconnaissance flying boat, Short developed the S.25 Sunderland from its well-known S.23.

The armament changed, and so did the balance

Chief designer Arthur Gouge had originally planned to fit a 37 mm COW gun in the aircraft's nose. Following feedback from the Air Ministry and the Royal Air Force, that defensive armament was revised down to a single 0.303 Vickers K machine gun in the nose turret and four 0.303 Brownings in the tail turret.

Four and a quarter degrees achieved with a spacer

After the initial flight tests, the aircraft went back to the workshop for further modifications: the 4° 15' wing sweep was achieved by fitting a spacer. That solution responded to the changes in defensive armament and shifted the centre of lift enough to compensate for the altered centre of gravity. The prototype, K4774, made its first flight on 16 October 1937.

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