To create a cantilever properly you will need to know plenty about physics like torque and rotational equilibrium.
How much should a roof overhang a gutter.
Greater overhang becomes a point of leverage for gusts of wind to rip off your roofing.
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.
Each has their own reasoning for a slightly different amount of overhang.
Here phil explains how much overhang a roof should have at the gutter.
You can add 3 to 5 inches to the top.
Unless the roof edge is quite uneven some shingles overhang significantly more than others it should have the same stickout all along.
This will keep rain away from your shed.
A shed overhang is an easy and effective way to protect your shed.
A typical metal roof overhang may be 2 to 4 inches or even less.
In my opinion the shingles should never be exactly even with the edge of any drip edge flashing.
Metal is usually installed on rafters or strip sheathing rather than the solid decking used under other materials.
Some slight overhang is recommended in conjunction with a drip edge flashing to prevent water from getting under the roofing and onto underlying wood.
Shingle manufacturers say to use a 1 4 to 3 8 inch shingle overhang over the eave where your roof ends.
About 1 inch just enough to assure the water goes into the gutter and not behind it.
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.