I'd recommend
My Sister's Funeral. Seems like that's the kind of manga you'll be into. It's not available here, so you'll have to look elsewhere. I might just translate it myself and repost it when I have time.
These might suit your melancholic taste, too.
https://mangadex.org/title/52573/after-you-ve-gone
https://mangadex.org/title/22425/three-video-messages
https://mangadex.org/title/55788/an-older-sister-supporting-herself-through-her-gill-breathing-little-sister
This one is not too sad: https://mangadex.org/title/54916/a-story-about-a-girl-who-supports-her-childhood-friend-s-love
I gave this a read and felt cheated on at the end. Nothing led to anything... :\