Actually OEW on in service 777-300ER's are more like 387,000lbs(175,500kg) and A346 are 190,000kg. And at that OEW the A346 is heavier than any passenger 747-400 I have seen. It's fuel burn per hour is also closer to a 747-400 than it is to a 777-300ER.
If you want to look at it from a OEW per seat pov, using the factory numbers the 777-300ER is the clear winner there, and disparity is evident when you look at real aircraft that are actually in service.
The A346 is locked in kind of a spiral of sorts,weight increases fuel burn and on and on it goes. The wing structure is very heavy and has a narrow margin of optimum efficiency. It had to be made very strong, stiff and subsequently very heavy because of the high wing loads it has to routinely endure. 777-300ER and A346 have almost identical wing areas, but of course A346 has a much higher MTOW...you do the math.
Also as for 777-200LR. Right now it looks like it could pull off that SIN
route with payloads of about 105,000lb Eastbound and 90-95,000lb Westbound. That about doubles what I've seen that SIA is getting on that route.