So both hands are roughly the same situation, so I'm just speaking generally about the situation and looking at how to obtain the most value. Obviously, I recognize that the situation will change according to table conditions and information on the player.

Hand 1: H has QQ. Raises preflop and gets one caller who is out of position to H. Flop is 45J (two clubs). V donks into H for 1/2 pot. H re-reraises 3.5x V's bet.

Hand 2: H has KK. Again raises preflop and only one caller. H again has position. Flop is 22Q (rainbow). V donks for 1/2 pot. H again raises 3.5x V's bet.

I'm looking for some comments about raising the donk bet. Is 3.5x too much? Is it not enough? Any useful comments are appreciated.

The only way for hero to open raise and to have position on villain is to be on the button so the caller is from the blinds. On both hands you should not raise but call as a default line.

OP was not 100% clear if it was an open raise against a blind or if V limp called.

I realize you said conditions will change based on more information. However, without that, I don't think we can have a good answer.

I would want to know:
1) How much did you raise preflop?
2) What was your exact position in relation to V. Could it be perceived as a steal attempt?
What V's cc range is
3) V's donk bet stat if you know.
4) V's cr stat

Seriously though, in both hands, what do you think V's range is?

Without stats and raise size I am guessing in hand 1 is maybe lower, middle pocket pairs. Medium to high suited connectors, AJo+. It possible he defended blinds with lower strength hands, maybe 45s in hand 1, but until further notice, I am not playing against just that.

I would expect a CR with his very strongest hands such as sets or trip 2s. I don't expect over pairs because a cold call would mean he plays it deceptively then I would certainly expect a CR.

If I was truly in the dark against an unknown player, or thought I was in possible danger against a know player and his AF is not too high (which I would not expect as such with no CR), I might min raise then take a free card to get to the river cheaply.

Sorry for the confusion. I tried to post this last night prior to going to sleep and clearly should have waited. I play in Nevada so no stats really since HUDs are illegal.

I will clarify both hands later when I can pull up my hand history.

I was a lot more tired than I realized last night. The hands were different then what I thought and indicated on the original post. So instead of trying to clarify on here, I just posted a new post.