Any background bias due to mass distribution would have to be too small to be relevant to probabilities of Penney's.

The probability of:

1. the total number of tosses it will take (for each of the eight possible sequences)
NOT
2. getting the sequence in three flips

YES we all know that for any random 3 flips, each sequence has equal probability of 1/8
For greater than 3 flips it is no longer equal, but that doesn't seem to explain everything.

Logic would suggest that:
"if no matter what sequence you choose, there is always one of the other seven that will beat it"
should lead to an infinite regression, but it doesn't, its like that voting paradox (for 3 people) when everyone beats someone and hence everyone is beaten by someone.

I came across this in an edx.org course on Quantum Mechanics dealing with 'spin'.

The video starts the explanation from the point of HH vs HT, and moves on from there.
The video is unlisted, but as the course can be viewed for free, and its a plug for the course I hope they don't mind.
https://youtu.be/rfzG7Iomfrg