It was short and sweet but Planet of Lana got me in the feels a little bit.
Patient Gamers
A gaming community free from the hype and oversaturation of current releases, catering to gamers who wait at least 12 months after release to play a game. Whether it's price, waiting for bugs/issues to be patched, DLC to be released, don't meet the system requirements, or just haven't had the time to keep up with the latest releases.
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Have you played Plague Tale 1 and 2? I'm not considered a very emotional person, but the dynamic really got to me. Just a really solid game, enjoyable combat. They're two of the very few games I binged to completion.
The House in Fata Morgana. Nice thing is that'll it be both sad and happy tears.
It's been a few years and listening to the soundtrack snaps me back. I only wish I could I could play it again for the first time.
In Bindinc of Isaac you cry a lot.

But on a more serious note. The Life is Strange series can be very emotional, if you like the style of the games.
Death Stranding
Detroit: Become Human had a really great character focused narrative where basically everyone can die. Give that one a go
Papers, Please. Maybe not crying, but could definitely put you into a depressed mood if you manage to get into character. Needing to make a choice between letting some poor bastard's wife follow him without proper papers and feeding your family is tough.
Persona 4 Golden is a beautiful game that made me emotional more than once.
Portal 2. But you should play the first part before sequel, if you haven't already.
Haven't actually played it yet but a video about MOTHER 3 made me cry just talking about the story (not only that but the part where he talked about the story made me a little emotional)
You may already know it but Omori was heavily inspired by the mother series and especially Mother 3: https://twitter.com/_omocat/status/1384687971929006080
Had a quick scroll through and didn't see it anywhere yet, so:
Dear Esther.
Actually, reminds me I should play through it again, it's been a few years.
Lisa: the Painful
I dont know if its listed here yet.
Probably gonna get hate for it but I'm a man in my 40's and some of the Genshin Impact story lines have left me in tears.
Rime is hauntingly beautiful in a way that hits you as it finishes.
Telltale Games Walking Dead. Not a game, but a whole series.