This is largely a matter of speculation, but one could say that "Sonnet 29," with its tone of hurt and self-pity, is a response by Shakespeare to attacks on his professional reputation as an actor and dramatist. In 1592, a rival playwright by the name of Robert Greene wrote a withering critique of Shakespeare, in which he essentially derided him as an ill-educated upstart who had no business being in the theater. If we regard "Sonnet 29" as autobiographical, then it becomes possible to interpret the poem as an expression of Shakespeare's despondency at such snobbish, hurtful criticism.
The speaker of the poem appears to be losing confidence in himself and his abilities due to the damaging effect that all this negative criticism has had on him. As is often the case when we feel our confidence undermined, we start to wish we were someone else, and the speaker's no different:
"Wishing me like to one more rich in hope, / Featured like him, like him with friends possessed."
If "Sonnet 29" is indeed a direct response to a particularly scathing critique, then there's little doubt that it must really have hurt Shakespeare an awful lot, as we can see from the very first line:
"When in disgrace with fortune and men's eyes / I all alone beweep my outcast state."
The speaker's so upset by being looked down on by others that he goes off and cries alone. Thankfully, the mood of despondency doesn't last for very long, and the speaker realizes that what really matters in this life is not other people's opinions, but the love of someone who cares:
"Yet in these thoughts myself almost despising, Haply I think on thee, and then my state, (Like to the lark at break of day arising From sullen earth) sings hymns at heaven’s gate; For thy sweet love remembered such wealth brings That then I scorn to change my state with kings."