What is the significance of the repetition? Does it mean that a 6 character key was used and repeated across the same characters within $P_1$ and $P_2$?
I'm assuming your assumption about this being an xor cipher with the pad used twice for two ciphertexts.
It does not mean a 6 character key was used. A one time pad used twice could result in this behavior.
It means that the first 6 characters of the first plaintext xored with the first 6 characters of the second plaintext results in
.81afg. Furthermore, the 2nd 6 characters of the first plaintext xored with the 2nd 6 characters of the second plaintext results in
.81afg. We also know where the bits in the two plaintexts are equal and where they are different, but we don't know what the bits are.
Now that doesn't help much, does it. If I had to guess, though, I would guess that there is a 6 character sequence at the beginning of each plaintext that repeats 6 times. If this assumption is correct, then we know that the sequence changes between the encryptions (otherwise we'd get all 0's). Remember though that this is just a guess.