The beginning of understanding Sidney's Sonnet 27 (sonnet cycle c. 1575-1585) lies in grasping the structure, as there may be several structures to sonnets. The structure of this sonnet opposes the English sonnet form that became firmly established in relation to Shakespeare's sonnet cycle (c. 1592-1598), though begun by Wyatt and Surrey.
First, Sidney writes this sonnet in a Petrarchan form in that there is only one volta, or turn of emphasis in the subject, whereas there are two in the English sonnet form used by Shakespeare and sometimes by Spenser.
On the other hand, Sidney employs the English sonnet structure for the ending, which is a rhyming couplet. Petrarch is said to never have used couplets to end a sonnet while the English form does dictate an ending couplet. Petrarch's form, with no couplet, is constructed as two quatrains (8 lines) and a sestet (6 lines). Sidney's Sonnet 27 has three quatrains (12 lines) and a couplet (2 lines). Each form arrives at the requisite 14 lines, but the structure allows for differences in contrast or continuity of thought and for paradox or flow of logic.
In Sonnet 27, there is no Petrarchan paradox in the first quatrains, though there is a paradox between the third quatrain (lines 9-12) and the couplet (lines 13-14) where Astrophil confesses to "ambition" then identifies this "ambition" as, paradoxically, aspiration for the love of Stella.
Now as to meaning, the first 8 lines are one continuous topic: Astrophil, the speaker, is so distracted and silently withdrawn from conversation in social settings that he is suspected and accused in rumors of suffering from pride. Remember that in this era, religiosity was all but universal and pride was counted a grave sin by virtually all:
... their doom the rumour flies,
That poison foul of bubbling pride doth lie
So in my swelling breast ...
Note the punctuation. The lines are either enjambed (no punctuation) or ended with a comma indicating a continuation of thought. Line 8 is the first with a stop of any sort, and it is in the form of a colon. The volta, i.e., turn in thought, occurs at line 9 after the colon stop, thus confirming the analysis of the first 8 lines being one continuing thought.
Lines 9-12 comprise a contrast to 1-8. Astrophil, in a contemplative tone ("Yet pride I think doth not my soul possess"), considers the accusations of pride against him then decides that his fault is not pride but one that is--in that era of religious dominance--even greater, that of ambition. He paradoxically exonerates himself entirely in the resolution couplet when he confesses that all his ambition is to secure the love of Stella.
But one worse fault, ambition, I confess,
That makes me oft my best friends overpass,
Unseen, unheard, while thought to highest place
Bends all his powers, even unto Stella’s grace.
PROSE PARAPHRASE (11-14)
But I confess to one fault that is worse; pride makes me so often overlook my best friends as though unseen and unheard while my thought, reaching to the highest place, strains all power to think of attaining Stella's gracious agreement of love.