Maybe it means it can be broken easily? You could tear it apart? IDK?

i think the song is about how hearts can be ripped into pieces, metaphorically of course. and hearts can be broken, and u hav different parts of ur heart for different things, and some people get close to u and they can break ur heart

I think it means hes in a really weird twisted relatioship, and that hes really emotional so he dosnt want to get hurt (paper heart)...so it might just be better if they brokeup beacause it then said tears fall from your face......irdk but just guessing

That hearts r as fragile as paper so i guess they where describing "paper hearts" and also about breakups and that one broken paper heart is enough.