I'm looking for a manga about a villainess who goes back in time to her academy days.

Apologies. The following details are somewhat sketchy because I'm having trouble remembering the details. The protagonist/former villainess is some kind of noble. Her father was forced to marry her mother, who was obsessively in love with him. He never loved her. After the villainess' mother died, the father married someone else and had a child with her. I can't recall but he might've been having an affair. Afterwards, he's cold to his first daughter, but her sister wants to get along with her. Unfortunately, her kindhearted sister is the heroine and thus her rival. After some point, the villainess goes back in time with all her future knowledge and decides she won't get involved with her former love interest, the first prince, nor get in the way of his relationship with her sister. In the previous timeline, the villainess was very obsessive towards the first prince. The villainess' childhood friend is the second prince, I think. He has a strained relationship with the first prince due to having a different mother with commoner blood I think - it hasn't been explained only hinted at.

I think either the villainess or heroine's name might've been Mery or Mary-something?

Unfortunately, I cannot recall the ending/event that forced her back in time.

The first chapter involves the villainess defending her sister from some other noble girls, which the first prince misinterprets as her bullying her sister. In a future chapter, like 1 or 2, the prince realizes he was mistaken and sort of apologizes to her.

After defending her sister, the former villainess loses her hanger-ons, but the people who shunned her like the first prince begin showing interest in her. The first prince also doesn't seem to be as interested in the heroine anymore. The heroine also seems more focused on getting along with her sister than chasing after love.

It's I Swear I Won't Bother You Again! its a webtoon based on the novel Kondo wa Zettai ni Jama Shimasen! (Novel), its really cute!

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Yes. This is what I was looking for. Thank you.