Sad stories not centered around romance/not having romance as a major part?

love or hate,

you're gonna love this ;)

Non-BL

~ The Horizon
http://www.mangago.zone/read-manga/the_horizon/
~ Deep Love: Ayu no Monogatarai
http://www.mangago.zone/read-manga/deep_love_ayu_no_monogatari/
Sequels:
http://www.mangago.zone/read-manga/deep_love_host/
http://www.mangago.zone/read-manga/deep_love_reina_no_unmei/
http://www.mangago.zone/read-manga/deep_love_pao_no_monogatari/
~ Sea Foam
http://www.mangago.zone/read-manga/sea_foam/
~ Lollipop or a Bullet
http://www.mangago.zone/read-manga/a_lollipop_or_a_bullet/
> Uncomfortable Truth
http://www.mangago.zone/read-manga/an_uncomfortable_truth/?F8kz
> My broken Mariko
http://www.mangago.zone/read-manga/my_broken_mariko/

Hope this helped