How is compassion shown in the poem?

Both the poetic speaker and the listener, the one to whom the sonnet is addressed, show compassion in acts of caring. In the octave (the first 8 lines organized as two related quatrains with an abbaabba rhyme scheme), the speaker acknowledges four specific acts of caring that show her beloved's compassion (and devoted love) for her:
He compassionately physically comforts her in her suffering by holding her hand, as act they both value and will regret the loss of: "When you can no more hold me by the hand,..."
He both makes plans for their future life together (suggesting they have never been able to marry) and compassionately tells her daily of these wonderful plans: "when no more day by day / You tell me of our future that you plann'd:..."
He gives her compassionate "counsel" to comfort her and guide to quiet thoughts that will sustain her through her suffering. Counsel intended to guide and strengthen is an act of compassion.
He compassionately prays for her. His prayers are undoubtedly for her recovery as well as for her endurance, strength and courage in suffering. These prayers are acts of compassion: "... remember me; you understand / It will be late to counsel then or pray."
In the sestet (the last six lines conveying a turn in the idea pursued--starting at the line 9 volta--with a cddece rhyme scheme), the speaker expresses her own compassion in three distinct acts of caring:
She compassionately and kindly acknowledges that, although she requests that he remember her after she is dead, he will forget: the distractions of life must draw his thoughts away from remembrance of her.
She kindly counsels him to not grieve when he forgets: "Yet if you should forget me for a while / And afterwards remember, do not grieve:...."
She consoles him by saying that if he forgets, her words, the "vestige of the thoughts that once [she] had," would remember her, so it is "Better by far [he] should forget and smile."
These two perspectives thus demonstrate the critically important theme of compassion as it is expressed in acts of caring. He acts from his compassion to comfort her, counsel her, pray for her, and she acts from her compassion to console him, comfort him and release him from guilt.