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.
Actually I think it was mentioned. In TSFS, when a lifeform is detected in Spock's cabin, the display says "Heavy Cruiser". See this pic: