Interesting observation. I wonder if it's related to the method the puzzle creator used to create the keys:
There is no pattern. It is just consecutive keys from a deterministic wallet (masked with leading 000...0001 to set difficulty)
IMHO I think it is. Even if the creator of the puzzle didn't do it purposly the software he used most probably was adjusted to generate the most complicated keys within the each given range.
Sorry, but I think your math is actually wrong. You are using the range 1..2^bit to calculate the occurrence in the range, but you should be using the range 1..(2^bit - 2^(bit-1)). That would explain why all your results are occurring at > 50% of the range.