This is an example of "alliteration". It is the fact that they both begin with 'b' that makes it so.
This may be pushing it, but as I think about this, it may also be a subtle example of a wonderful figure of speech called 'hendiadys'. The word means one [hen] out of, or through [dia] two [dys].
The common example of hendiadys is "cups and gold", an alternate way of saying "golden cups" by expressing the idea with two neighboring nouns instead of a noun and adjective. If the expression "beauty and brains" can be felt or understood as "beautiful brains", then hendiadys works. It seems that thinking of it this way enhances the meaning of the phrase.
Emdrgreg