A similar capasity Boeing 777-300ER has an OEW of 366,940 lb, (166,881 kg). That is about 30 tonnes more you have to hop around. More then the weight of the 350 passenger payload.
The 777-300ER is powered by 110-115lbs engines to accomplish the long haul polar missions it is designed for. Far more then neccesary for short / medium routes.
But there is the non-ER 777-300. What is wrong with this?
# new generation engines GENX / RR Trent, reducing fuel consumption with xx%.
# additional 50 seats on topof the A333/772
# a higher MTOW / strenghtened wings structure then the A330-300
There is a reason Airbus stretched A340, not A330. One reason is that there is not enough space under A330 wing for two engines bigger than those of A330-200/300. For the same reasons, A330 cannot use the big high-bypass engines of A380, even though they have similar thrust.
What about, say, A350-700, with fuselage of A350-900 or A350-1000 and shrunken wing and engines?