You are beautiful, child, beautiful.
You are beautiful, child. Beautiful.
How should I punctuate the above sentence?
Both are acceptable, with the second one having a longer pause before the final beautiful.
It is true that, in general, punctuation and prosody are imperfectly correlated. But in a case like this, which seems to be reported speech (or possibly emulation of speech), the period will be interpreted as a longer prosodic break than a comma. So one answer is, use the one that better corresponds to how you would say it.
As far as which one you should say, that depends on what effect you want to have and on the broader context. The second one puts more emphasis on beautiful, and makes it sound more earnest. The first one sounds as if it is a comment about more than just the beauty—like the rest of the message is still to come.