Is the 14.7 a total coincidence?
The "ideal mixture" on a weight-to-weight basis depends on the type of fuel you use.
For example, consider using hydrogen (H2) as your fuel.
Two mols (a particular number of molecules) of hydrogen gas weighs about 4 grams. It will burn at the exactly correct mixture with one mol of oxygen.
One mol of oxygen gas weighs about 32 grams.
In this example, the "stoichiometrically correct mixture" for hydrogen burning with oxygen would by 4:32 or 1
(that should be "one : eight" - not a funny face!) by weight.
Avgas is a complex mix of different hydrocarbons, and air is a mix of (mainly) oxygen and nitrogen. If you get the exactly right number of mols of avgas and the exactly right number of mols of air, it will happen to work out at 14.7 to 1 weight to weight.
Cheers,
O8