The story is fine. Doesn't take itself seriously, it's just there to propel you along to then next fantastic bit of gameplay. I think it got the ratio just about right in terms if story verses gameplay, something that Capcom hasn't replicated since. 5 & 6 take themselves way too seriously, and some chapters of 6 are almost all cut-scenes. 4 is funny, but, apart from the Regenerators isn't scary at all.
Seems like 7 will be a serious game, I'm not expecting much cheesy dialogue, but as long as it delivers as a game it doesn't matter - hopefully this one will have some scares.
I find the whole "playing video games for story" kind of ridiculous, but that's probably because I'm old (and have read too much Hemingway).