Here's how I see it:

Elinor starts from a position of having loved W as a brother (Ch.16- " I love Willoughby, sincerely love him..") This is later tempered by her anger and disgust at him over his treatment of Marianne and Eliza.

She believes Willoughby is sincere when he says that he was sincerely fond of Marianne and that he wished to marry her rather than just seduce her like he did Eliza.

She is pities his unhappiness.

Willoughby says he has come to offer his explanation and apology, and that he hopes for for forgiveness. To refuse to accept his apology because it wasn't good enough would be gaceless and grudging. Also, Elinor and Marianne are Christians. As such, forgiveness is part of their religious duty. As The Lord's Prayer puts it:

"... and forgive us our trespasses (sins) as we forgive those who trespass against us."

Elinor is not immune to Willoughby's charm/charisma, which I think has as much to do with the warmth and eagerness of his manner as with his good looks. After Willoughby has left Cleveland Elinor thinks she was swayed too much by this and has let him off too lightly.

I think all these factors play into Elinor's forgiveness of Willoughby, which I think is sincerely meant. However, I suspect that she may also have chosen not to withhold forgiveness because that might delay his departure, and she is eager for him to leave because her Mother & Col. Brandon are expected at any moment.