B747 Flight Crew reports on a flight that departs late due to maintenance then must divert for fuel due to weather; resulting in a 21 hour duty day.

Narrative

Report time came and went and we had no flight plan or any other flight papers (weather; maintenance history; etc.) until about 20 minutes after report. There was neither significant weather (so no alternate required if redispatch within 6 hours) nor maintenance deferrals to note. We were planned to arrive with about 26;000 pounds of fuel remaining. We all performed our cockpit duties and were ready to go at departure time. A lighting problem was identified by our flight attendants right around departure time. The fix took about 25 minutes. After takeoff; the other relief pilot and I took the first break. When we woke from our break; the changeover briefing included a new weather situation developing. There was a possibility of fog putting our visibility below landing minimums. Also; the airplane was burning fuel a bit faster than forecast (we had a negative fuel score.) The Captain briefed us to not hesitate to wake him should a divert decision or redispatch problem be presented. We started working with the Dispatcher with respect to our new weather report; to include SATCOM communication. The Dispatcher wished to change the redispatch fix to later in the flight to give us more time to make a decision. We agreed to the change in redispatch point. During our information exchanges with Dispatch we got informational flight plans; updated weather; and a SIGMET. The informational flight plans showed different arrival fuels for ZZZZ ranging from okay to too low. The SIGMET showed an area of forecast severe turbulence between the later phases of our flight plan and ZZZZ1. Approaching abeam ZZZZ1 we woke the Captain. He then spoke with the Dispatcher on SATCOM. The main point of this conversation was that the weather services were pretty sure that the fog was not going to happen; but they wouldn't rule out the possibility altogether. Considering our current fuel state; the negative fuel score; plus even the remote possibility of fog at destination; it seemed the safest course of action was to get some fuel in ZZZZ1. It was at this time the Captain instructed us to get a clearance to the divert airport. The flying time from this point was about an hour. Approach and landing were uneventful. We thought we would have a quick gas n' go. I performed the walk-around immediately after arrival and about halfway through that walk-around the fueling person showed and hooked up to the aircraft. There was a question of payment to the fueling company and this delayed the start of fueling for over an hour. The fuel payment question was resolved so the aircraft was fueled and the remaining flight to ZZZZ was uneventful.