B737-800 Captain reported a flap malfunction and divert to land at the nearest suitable airport. The reporter also stated the software app to access the QRH is burdensome.

Narrative

Diverted to ZZZ1 due to a LE Flap Transit light accompanied by a fully extended indication for the #4 Leading Edge Flap segment. After flap retraction was complete departing ZZZ2 (flaps indicated fully retracted; LE Flap Transit light out); the LE Flap Transit light came back on; accompanied by the green fully extended indication for the #4 Leading Edge Flap segment. The First Officer (FO) continued to fly; and I ran the Leading Edge Flaps Transit checklist in the Quick Reference Handbook (QRH). We followed the checklist; which directs you to cycle flaps to 1; and back to off. This step did not clear the malfunction. The checklist directs a flaps 15 landing; and calls for a Non-Normal configuration landing distance. Since we had run the QRH; and were computing a non-normal landing distance; we decided to divert to ZZZ1 vs. returning to ZZZ2 or continuing on to ZZZ3. We [requested priority handling] with ZZZ (QRH + Non-normal landing made this seem like the right choice). They put us on the ZZZZZ arrival for the ILS Runway X. Descent; approach; and landing were uneventful. I had the FO land the aircraft. Aircraft configuration was normal for a landing. We lowered the landing gear about 1/2 way to ZZZ1 to reduce landing weight; about 155000 lbs. at take-off. I referenced the Overweight Landing checklist; and computed landing distance about 6000 ft. at 150000 lbs. landing weight. Actual landing weight was 149000 lbs.; touchdown was normal. I made MEL entries for the flap malfunction and the overweight landing. I had coordinated the diversion with Dispatch via ACARS during the flight; and I called to discuss the event after landing to include the overweight landing. We changed aircraft and continued on to ZZZ3.Weather at ZZZ2 was heavy rain; wet runway; braking action medium on arrival. Based on the ZZZ2 weather; we had pre briefed using ZZZ1 as our recovery base for a malfunction on take-off. ZZZ1 had been our alternate for the flight inbound to ZZZ2; so we had relatively current ZZZ1 weather and NOTAMs available. Two procedural suggestions for the QRH as posted. Need to be able to access this document without entering any passwords or login information; period. Company asking for a login when you NEED the QRH is decidedly not helpful. A more easily usable 'page back' function would be extremely helpful in the aircraft. The small arrow prompt in the bottom corner of the page is not very user friendly.