Each of the three parts has its own epigraph:
First, let's take the epigraphs one by one; and then, let's put them all together:
(1) Yang Yuan was a Chinese beauty contestant who argued in 2004 that she should be allowed to be surgically enhanced and still enter a beauty pageant. And this is pretty much Tally's position at the beginning of the book: shouldn't everyone be pretty?
(2) Francis Bacon's short essay "Of Beauty" appeared in the second edition of his 1612 Essays, Civil and Moral (with a title like that, it must've sold like hotcakes, which is why they printed a second edition). This idea starts out the second section of Uglies, when Tally tells herself that David is hot stuff even though he hasn't had any surgery. In other words, she starts to see Francis Bacon's point: prettiness can't be too regular, like the prettiness that comes out of the surgery.
(3) Archibald MacLeish was a famous poet and less-famous librarian. This poem "Beauty" (1) is only called that because that's the first word; and (2) appears in his 1924 book The Happy Marriage. Now that we've got those silly facts out of the way, what does this poem mean?
First, the reference: the Medusa was the mythological Greek monster with snakes for hair and the ability to turn people into stone. (Ability or curse, whatever.) In the myth, Perseus chops off the Medusa's head but uses the head as a weapon since it can still turn people to stone.
So MacLeish here makes the connection between the Medusa's head (dangerous even when dead) to beauty. Perhaps this means that the ideal of beauty is dangerous, even when we think we've beaten it. That would certainly fit in with this story, where Tally has given up her dream of being pretty, but still has to deal with the rest of the pretty world (Dr. Cable, a pretty Shay, etc.).
Taken all together, these three epigraphs nicely chart Tally's feelings about being pretty: (1) she starts out thinking everyone should be pretty; (2) she start thinking that beauty can't be factory-produced; and (3) she ends up feeling that beauty can be a dangerous idea. (Not as dangerous as scissors, maybe, but still dangerous.)
Nice work, Westerfeld.