The more specific instance of beauty, which is the subject matter of the second quatrain, is, of course, the young man. The word thou (meaning you) refers to the young man. The speaker is directly addressing the young man and is complaining that the young man is married ("contracted") to his own bright eyes (line 5). In other words, the young man is in love with himself. He only likes to look at himself and is not looking at any particular young lady. The line suggests the Greek myth of Narcissus, a story of beautiful young man who saw his own reflection in a pool of water and fell in love with himself.
The metaphor in the next line (line 6) can be interpreted in perhaps several different ways. The word flame suggests, most likely, the idea of passion. The young man is feeding his passions or desires for love on himself ("self-substantial fuel"). By expressing the idea in this manner, the speaker is suggesting that eventually the young man will burn himself out. In other words, he is wasting himself needlessly.
The idea of waste is emphasized in the next line. The young man has an "abundance" of passion. But once that passion is entirely burnt away, there will be a "famine" (an emptiness) of passion -- there will be no passion left. Of course, the denotative (or literal) meanings of the words also apply. Why starve (why experience a famine) when there is plenty of food (an abundance) available? Such an act would be foolhardy, and the speaker is suggesting that the young man's actions in not finding a mate