I can't tell you why the 777 does not have winglets, but I can tell you why the -400 does.
One of the goals Boeing had for the -400 was an increase in TOW. But one of the constraints was to keep the footprint the same. One method would have been to redesign the wing. This was given up as too expensive (20/20 hindsight maybe that was the best option). So another 12' had to be added to the wing span to accomodate the 20 tonne increase in weight. That's where the winglets came from. It gave the-400 the ability to increase it's TOW and yet have the same footprint as the 200/300.