i'm not sure what you mean, but here you go. it's a mixture of genres so just take your pick, if these are what you are looking for.
Stories that are heavy and weighed in my heart for some time:
http://www.mangago.zone/read-manga/the_horizon/
http://www.mangago.zone/read-manga/zankoku_na_kami_ga_shihai_suru/
http://www.mangago.zone/read-manga/rengoku_no_karma/
Stories that made me cry at certain points or have at least made me sad but have other genre focuses.
http://www.mangago.zone/read-manga/hotarubi_no_mori_e/
http://www.mangago.zone/read-manga/a_sea_of_conflicts/
http://www.mangago.zone/read-manga/act_age/ it's a long story, and just an ending of a certain arc made me cry.
http://www.mangago.zone/read-manga/july_found_by_chance/
http://www.mangago.zone/read-manga/life_senjou_no_bokura/
http://www.mangago.zone/read-manga/broken_season_revised/
http://www.mangago.zone/read-manga/from_nightmare_to_love/
http://www.mangago.zone/read-manga/17_years_old_that_summer_days_miracle/
http://www.mangago.zone/read-manga/this_witch_of_mine/
http://www.mangago.zone/read-manga/boku_wa_nando_demo_kimi_ni_hajimete_no_koi_wo_suru/
http://www.mangago.zone/read-manga/3_level_combination/
It is underrated but it is so sad..
Also December rain
this one made me cry yesterday:
http://www.mangago.zone/read-manga/kowagaranai_de_soba_ni_ite/
http://www.mangago.zone/read-manga/work_fight_and_love/?av=2
One of my favorites. Pain comes halfway through the story. Heart broke so many times ╥﹏╥
http://www.mangago.zone/read-manga/lover_boy_lezhin/?av=3
http://www.mangago.zone/read-manga/mou_ichido_nando_demo/
Recommend me some manga/manhwa where it hurts. You know... that has some moment that hurtss in your chest