The speaker here is commonly thought to be the Fair Youth of many of Shakespeare's other sonnets, and in the first 8 lines of Sonnet 29, he is in a serious state of despair. Both fortune and men hate him; indeed, he is in such a solitary state that even God and Heaven are deaf to his cries of woe. Apparently our young man is poor, hopeless, friendless, ugly, and lacking in talent because he envies those who are rich, hopeful, popular, good-looking, and talented. He cannot find contentment in anything he used to like to do and is at a point of self-loathing. Until--and here is the larger point of the poem--he remembers someone who loves him, and the remembrance of that love reminds him of how rich he truly is. He is so rich, in fact, that he would not trade places with a king!
In this sonnet, the speaker envies a lot of things.
- He envies people who are more hopeful than he is.
- He envies someone who is, presumably, better looking than him.
- He envies people who are surrounded by friends.
- He envies one man's skills
- He envies another man's freedom
But overall, really, what he envies is not such a big deal in this poem. What's really important is that when he thinks about his love, all of his envies and all of his discontents fade away. So in that sense, the envies are just a set up for what's really important in this poem.