Both tyre size and tyre pressures play a part in this. Low tyre pressure increases rolling resistance which is something you have to overcome to maintain speed, so the more resistance = more fuel consumed.
The larger the tyre, the higher your final drive ratio. The gearbox & diff ratios were chosen with 255/70R16 tyres and if you increase the size, you increase the ratio, so the car will not perform as well off the mark and the engine will use more fuel to get moving.
What the exact changes are will be a guess, as Krafty says.