not that ANY of the following matters other than for curiosity's sake ...
a guitar that's concert tuned to A-440 pitch using .011 to .048 gauge strings will have the high .011 "E" string at about 19.6# tensile strength and the low .048 "E" string at about 21.3# tensile strength and 2 octaves lower in pitch.
if you increase the tension on the high "E" string 1.7#, to the same tensile strength as the low "E" string, the note produced by the smaller string is higher in pitch (the note goes from "E" to perhaps "F#" or "G").
i think that best simulates what happens with a "skinny" bowstring - the skinny string tension remains the same as with a "fat" string, assuming the limbs are the same and the same brace height is achieved, and that will create a higher note on that skinny string.
so why does the skinny string sound quieter than the fatter string?
my thinking is that the deeper resonant tone, with more pronounced volume, of the fat bowstring is, like with stringed instruments, is easier to perceive, easier for the human ear and body to pickup.
the skinny string will have a higher pitch, but with lower volume and so harder to hear and/or perceive. this is the exact same for stringed instruments. ask me how i know this.