I've met several such situations that a player puts many support cards on Quest or Kingdom, which leads to the fact that he can draw almost 8 cards or takes 8 resource tokens when it's his turn. I'm just wondering, will this make the game unbalanced because it seems it's making an already stronger opponent even stronger each turn. How can one remove his opponent's support cards to prevent such tragedy?

In general, support cards are harder to remove than units. There are ways to remove them though, individually (Demolition!, Pillage, Rodrik's Raiders, etc.) or at large (Judgement of Verena, Grimgor Ironhide). You'll find that Order is better at this than Destruction. Dark Elves and Chaos usually have to rely on Burn it Down as their only form of support removal, but the Dark Elves' Withering Hex can serve a similar purpose.

So there might not be too much you can do about it, but if your opponent's deck is heavy on supports, it's lacking in units or tactics. That he has a lot of hammers in kingdom and quest won't help him if he can't properly defend his zones due to a lack of units (because he hasn't got enough, or because you keep removing them, which Destruction is good at). Or if he can't finish you off fast enough before he draws his whole deck. Also, someone sitting so comfortably might be a sign of inexperienced players and the long, drawn-out games they tend to have. Try using cheaper units and putting the pressure on early.

Mallumo said:

I just bought three big expansion boxes today. This game is just fantastic. Thank you for your help and I think 'cheap units' may work out my problem.

When you are only playing with 1 core set, support cards seem a lot more imbalanced, because there are almost no ways of destroying them.  And some factions have decided better support than others.

Another thing to remember is that support cards can not attack or defend. And playing too many support cards against fast decks like Orcs will make you lose very often, just because you wouldn't have much of a defense.

So the question is: how soon did the person reach those 8 resources/8 cards and did he/she have enough cards/resources to spend those.

Plus, there are some tactics, which do bad things to people who develop quest too much (Infiltrate: Draw only 1 card this turn) or Kingdom (Asuryan's Cleansing: Cancel and Discard Target Support/Unit being played unless Opponent spends all resources)