How Far Should A Roof Overhang A Gutter

Some slight overhang is recommended in conjunction with a drip edge flashing to prevent water from getting under the roofing and onto underlying wood.
How far should a roof overhang a gutter. Anywhere from a 1 2 to a 1 overhang is acceptable as you can tell from the varying comments amongst the previous posters. In my opinion the shingles should never be exactly even with the edge of any drip edge flashing. A typical metal roof overhang may be 2 to 4 inches or even less. The back edge of the gutter should tuck up behind the dripedge if you have it otherwise the edge of the shingles should extend well over the back half of the gutter so the drips cannot get behind it and rot the fascia board.
The brackets typically hold the gutter about 1 2 1 inch away from the fascia board if u type brackets otherwise if screw through type the gutter might be almost up to the fascia board. Each has their own reasoning for a slightly different amount of overhang. Metal is usually installed on rafters or strip sheathing rather than the solid decking used under other materials. For rainy climates where gutters will handle a larger amount of water for long periods they should have a maximum distance of 18 inches apart between them.
A typical gutter flashing l shaped usually has a 2 1 2 face however we often custom bend out own for situations where we need to cover more than 2 1 2. Greater overhang becomes a point of leverage for gusts of wind to rip off your roofing. Most drip edges have 1 1 2 face and that 1 1 2 is not enough to cover the back of the gutter especially since by your own admission it is a 2 drop. About 1 inch just enough to assure the water goes into the gutter and not behind it.
Not good to start off with a new roof and gutters with this problem built in. The reason for this is that whenever rain runs down any type of roof when it gets to the lower edge it clings to the tile or slate by capilliary action this means that the water actually runs around the bottom edge and slightlly back up the rear of the tile before gravity allows it to drop into the gutter. The bottom tile or slate of the roof covering should project at least half way into the gutter the ideal distance is between half way and two thirds of the way over.