What are Heirs? Each Heir you have reduces the number of points of your highest scoring victory card by 1. So in Colony games, colonies are worth 9vp if you have one heir; If you run the Castles pile, the King's Castle will be worth 1 less. If it's a regular province game, and you get eight heirs, those provinces are worth 0vp.
This raises multiple questions, most of which I think I know the answer to, but at least one of which I don't.
(1) You said "Each Heir you have reduces the number of points of your highest scoring victory card by 1." Do you mean individual Victory card, or differently named card? That is, if your Victory cards are 4 Provinces and a Duchy and you have 2 Heirs, is that worth 25 (taking 2VP from one Province) or 19 (taking 2 VP from each of the Provinces).
I THINK THE ANSWER IS: You also say "If it's a regular province game, and you get eight heirs, those province
s are worth 0vp." So it does seem clear that each copy of the highest scoring differently named Victory card is weakened.
(2) You say "in Colony games, colonies are worth 9vp if you have one heir; If you run the Castles pile, the King's Castle will be worth 1 less." Do you mean " . . . King's Castle will be worth 1 less
instead"? Also, am I correct in understanding that Colony is only worth 9VP if you have one? If your highest scoring Victory card is a Province (even in a Colony game), then that is what is reduced.
I THINK THE ANSWER IS: Yes. When you said Colonies were worth 9VP, it was inferred from the context that Colonies would be a player's highest scoring Victory cards.
(3) How does this work with
scaling Alt-VP cards like Gardens, Fairgrounds, Vineyard, etc.?
I THINK THE ANSWER IS: When scoring at the end of the game, you see what each such card is worth. If any end up being the highest-scoring VP card(s), that/those are affected by the Heirs.
(4) What happens if two different VP cards tie for the highest? This might happen if you managed to rush the Harems, Nobles, and Islands piles, but it is much more likely to happen using Alt-VP. It is not at all unusual for Fairground to be worth 6 VP (if the player can get 15 differently-named cards, something very possible on many boards). If a player has 2 Provinces, 7 Fairgrounds each worth 6VP, and 2 Heirs, do the Heirs reduce the VP value of (a) the 2 Provinces, (b) the 7 Fairgrounds, (c) all 9 Victory cards (d) either the Provinces or the Fairgrounds depending on some additional criteria (although I am not sure what that would be)?
This one I genuinely do not know the answer to. I suppose the most obvious answer is (c), but that makes what is already an almost unbearably harsh mechanic even worse. That being said, I don't really have a good way to pick between (a) and (b).
However you deal with ties, the existence of scaling Alt-VP also creates the possibility that increasing your underlying VP could actually result in losing VP. For example, if you have 5 Vineyards, 1 Province, 16 Action cards, you would have 31 VP. If you also had 4 Heirs, you would have 27 VP. If you then bought the Event Populate and gained 7 Action cards, without the Heirs, you would go from 31 VP to 41 VP. However, with the Heirs, you would go from 27 VP to just 21 VP. While this seems like an unlikely scenario, I actually don't think that it is, because I would guess that if you are going to take Heirs, the only viable strategy will generally be to buy 1 Province/Colony, and then try to win with Alt-VP. This puts the player in the position of having to very carefully track the value of their scaling card, as making it go too high could cost them the game.