I am probably repeating data already in other answers, but since you specifically asked me, here is my answer.
The inside story in Boeing is that the planes like the 757 or the 767 with winglets are limited in wingspan to fit into the gates at smaller airport terminals. Winglets help them to get better performance from their short wingspans and reduce the wingtip vortices, reducing drag and netting up to 5% in fuel economy and reduced carbon dioxide emissions. But the 777 is deigned for larger international airport terminals that can accommodate the larger wing span. The 777, not being limited in wingspan, was not the design compromise that you had in the 757 and the 767. It already has a raked wing tip and won’t benefit from winglets enough to be worth the extra weight or the loss of lift during take off and landing. (I am also aware of recent developments in dynamic winglets that have a computer control the flight characteristics in real time to reduce the loses during climb out and high g-load events, for example, and make the winglets economical where fixed winglets are not or [where fixed winglets] would subject the wing to adverse loads. See Tamarack Active Camber Surfaces, for example.)
I know you will find that some 747s and MD11s were retrofitted with winglets. There was only about a 1% performance improvement on those planes. But I never got a clear answer on why there was any improvement, because the jumbo jets clearly had all the wingspan they could want. Perhaps it is just that computational fluid dynamics software is so much better now than it was in the days in which 747s and MD11s were designed. I heard people made that last statement, but I did not really feel it was more than a guess.
If this repeats other answers, my apologies.