in -> inner
out -> outer / (outter?)
What is the history or set of rules behind why 'inner' doubles the 'n' but 'outer' doesn't double the 't'?
Many English words have a double consonant when following a short* vowel. Consider "biter" and "bitter": the double-t signals that the vowel should be the short i vowel. Thus, you write "inner".
For "outer", "out" is already a two-letter vowel, so it doesn't change sound when you add on other letters at the end, hence "outer".
*I'll call it a short vowel because that's what I was taught in grade school. A real linguist can edit this post or comment about what the vowel is really called.