What would you call the level below "heavy"? I'd imagine if you asked most people the scale would go something like "nondrinker", "light drinker", "moderate drinker", "heavy drinker", "full blown alcoholic". If so then 14 drinks per week is the upper end of "moderate".

I'd expect it also depends on how you drink it. One restaurant-pour glass of wine with dinner every day adds up to 14 drinks a week but no reasonable person would call it "heavy drinking". (Yes, plenty of people here are saying that it is. No, they're not being reasonable.) I'd expect drinking 14 drinks in one night once a week would absolutely count as heavy drinking, though.