How does the speaker's mood change in lines 9-14 in Sonnet 29?

In Shakespeare's lovely Sonnet 29, the author uses the structure of an English sonnet (also known as an Elizabethan or a Shakespearean sonnet) to organize his ideas.

This kind of sonnet has a total of three quatrains (four-line stanzas) and ends with a rhyming couplet (the last two lines). In the first two quatrains, the speaker presents his initial response to life in general:

When, in disgrace with fortune and men’s eyes,

I all alone beweep my outcast state,

And trouble deaf heaven with my bootless cries,

And look upon myself and curse my fate,

Wishing me like to one more rich in hope, 

Featured like him, like him with friends possessed,

Desiring this man’s art and that man’s scope,

With what I most enjoy contented least . . .

The speaker reflects on life—all alone he feels sorry for himself, an outcast. He calls out to heaven but feels that even God ignores him ("deaf heaven"). He looks in the mirror and curses his life—perhaps his job, his social status, etc., and spends time wishing that his circumstances were like someone else's that appears to have more to hope for, or is better looking, or has better or more friends. He wishes he was more talented and perhaps more intelligent ("scope"). He ends the second quatrain stating that in the things he most enjoys, he finds the least contentment.

However, the mood changes at the start of the third quatrain with the pivotal word "yet," which is the equivalent of saying "but." It sends a signal of a major transition, as if he has been moving in one direction and abruptly turns and changes his course entirely. Unexpectedly, he states that even as he almost hates himself, there is something that stops his negative rant. The key word in his change of mood is found at the beginning of line 10, with "haply" (meaning happily).

"Yet" causes the reader to pause, while "haply" swiftly redirects the reader to a more positive reflection by the narrator. It is here that one feels the sun has come out from behind a very dark cloud, as he thinks about the woman he loves. 

Yet in these thoughts myself almost despising,

Haply I think on thee, and then my state, (10)

(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.

When he thinks about the woman he loves, his feelings soar; he compares his sudden change to a bird speedily flying to "heaven's gate" at daybreak to sing hymns (songs of praise)—having left the somber earth (as well as his attitude) behind.

In the last two lines of the sonnet, Shakespeare uses the rhyming couplet to summarize the main idea of his message: when thinking about this woman's love, the speaker feels like the wealthiest man on earth; so much so that he would not change places with a king!

As is the case with many sonnets, the underlying theme here is love. From the Italian word sonnetto (which means "little song"), it makes sense that the sonnet is a 14-line, musical poem (with the rhythm and the sonnet's end rhyme) that conveys a man's utter joy in being loved by a woman who is more valuable to him than anything else he could wish for.

Additional Source:

Adventures in English Literature, Harcourt Brace Jovanovich Publishers: Orlando, 1985.