I have an interpretation, but I'm wondering if anyone else has a thought on this:

I have 1 copy of Elven Light (or Lords of the Eldar) in my discard pile. During the quest phase Heavy Curse is revealed and put on the quest card. Does EL now cost 2 to play? I'm assuming yes, since the check for play cost would occur before the card could be played at all.

Any other thoughts?

I agree that it would increase the cost because in order to play the card you must first pay its cost. Since it is still in your discard pile when you have to pay the cost, I believe Heavy Curse should increase the cost.

I think yes, it will cost 2. This happened to me when I played Dread Realm and that's how I played it.

Agree. The cost is two unless you get a second Heavy Curse on the quest card and then it's three.