[...] listen all of you together to these my mournful, my last words (12-13)
Just in case you're not sure about the tone of this poem, Petrarch thoughtfully spells it out for you. But don't be concerned about that last line. These really aren't going to be his last words. We know this because he goes on to pen another 240 poems.
If it, indeed, must be my fate, and Heaven works its ways, that Love close up these eyes while they still weep, let grace see my poor body be buried there among you and let my soul return to its home naked (14-19)
Yup, he's gone there. When all else fails a miserable lover, he or she has to go for the death fantasy. It may be a poetic convention, but most of us have probably taken this same psychological trip at one point or other.
[...] and—ah, the pity— to see me there as dust among the stones, Love will inspire her and she will sigh so sweetly she will win for me some mercy and force open the heavens drying her eyes there with her lovely veil (33-39)
This is the real reward for Petrarch imagining his own death. "Won't she be sorry when I'm gone?" should really be a sanctioned genre for poetry. Petrarch knows that death won't bring him any closer to physical enjoyment of his love. At this point, he'll settle for knowing that Laura has an emotional response to him.
[...] and since then I have loved this bank of grass and find peace nowhere else (64-65)
Some people have stuffed animals as their comfort object. Petrarch has a grassy bank. We're not here to judge. However, we will point out that Petrarch is particularly attached to places in poetry. Laura's presence is imprinted in them, so it brings the poet comfort when he can't have his girl.