She is genuinely upset and cries, but she also believes that she must and ought to be upset and crying in this situation.

We saw this earlier when Marianne and her mother kept renewing their grief over Mr. Dashwood's death. " The agony of grief which overpowered them at first, was voluntarily renewed, was sought for, was created again and again. They gave themselves up wholly to their sorrow, seeking increase of wretchedness in every reflection that could afford it, and resolved against ever admitting consolation in future."

Yes, they genuinely grieved his death, but they also believed that the way one 'ought' to act in this circumstance was to be inconsolable, and so they kept 'voluntarily' renewing and creating their wretchedness over and over.

This is much the same as what she does when Willoughby leaves.

"She played over every favourite song that she had been used to play to Willoughby, every air in which their voices had been oftenest joined, and sat at the instrument gazing on every line of music that he had written out for her, till her heart was so heavy that no farther sadness could be gained; and this nourishment of grief was every day applied. She spent whole hours at the pianoforte alternately singing and crying; her voice often totally suspended by her tears. In books, too, as well as in music, she courted the misery which a contrast betwen the past and present was certain of giving. She read nothing but what they had been used to read together. "