The Star Trek Fact Files that I collected as a kid say that the Enterprise NCC1701 in the original timeline was a Heavy Cruiser
Yeah, but this was never mentioned on screen. The closest we got is in TSFS when the Klingons call 1701 a Federation battle cruiser.
True but the Fact Files are official and canon, and I see no reason to doubt it.
Edit: Memory Alpha also says the same.
Edit Edit: Memory Alpha also confirms the NuEnterprise as a Heavy Cruiser as well.