QQ vs 4% of hands is about 56% equity so right off the bad im not too thrilled about 3betting. Id have to look at his f3b and make my decision. If he 4b me then id probably have to dump it as i think this type of player only stacks off with AA and KK maybe but much more unlikely AK. If he calls a lot of 3bets then we should be ok here but still not awesome.
Id cbet bigger on the flop as his range is going to be TT+ and AQ and AK here most of the time and he will never fold any of those hands. Id bet the turn again and fold to a raise and probably x back the river or bet really small to get A high to call as i dont think any worse hand is calling a river bet.
As played id have to call the river because vs A high and made hands we are about 50% and he is giving us odds
. I do think he could be betting A high here as well.
I think the biggest issue though is whether or not to 3b this hand.