It’s not short, but the first chapter is pretty much a self-contained story, so if you want a quick cry I can highly recommend this (or even the anime)
https://www.mangago.zone/read-manga/to_you_the_immortal/
If you were looking for BL, this one’s pretty good, and is multiple stories;
https://www.mangago.zone/read-manga/ashita_shinu/
If you want to bawl I recommend reading Hamin's Flower https://www.mangago.zone/read-manga/seasons_of_blossom/ (starts at chapter 31) It goes for 30 chapters
There are 4 seasons, each with a different protagonist so you don't have to read the chapters before. Just know that the first arc is a light-hearted school romance between tall-girl x short boy who don't really show up Hamin's Flower but there's a cameo of the new protag at the end of 29 so I think it's better to skim that first.
Oh and there's this one shot https://www.mangago.zone/read-manga/sea_foam/
10 years where I loved you the most
https://www.mangago.zone/read-manga/10_years_where_i_loved_you_the_most/
Home far away, it's a one-shot with 6 chapters
https://www.mangago.zone/read-manga/haruka_tooki_ie/
I feel like crying today. Give me a short story where its gut wrenching and will make my heart break. I’m listening to loml from taylor swift and I need to feel sad