Hmm... ok maybe i should be a bit more concise and explain myself a bit better.

The facts:

1. Villains likely hand range is JJ or KK.
2. KK is twice as likely as JJ (combinations).
3. A raise against JJ is twice as costly as a call against KK.

Thus: If you assume that the range is KK and JJ ONLY, and that each hand makes perfect sense from the villains perspective, then the raise and the call are dead even plays. (Note: Folding is ridiculous here).

What Im suggesting is that the other possible factors all lean towards you being ahead here:

1. From how the hand was played, KK is MORE likely to be played this way than JJ. The Q was MORE of a scare card for KK than for JJ given the second level analysis in my last post (Ah go skim it i know its long, the bit about the scare card rational is at the end haha).
2. The other MISPLAYED (by vil) hand possibilities that your ahead of are hands you are far more likely to be ahead of than behind. A8s and QQ are the only misplayed possibilities that you lose to. But: TT, 99, AJ, AQ and even AK are all hands that would and could regularly be shown here at this level.
3. The times where he has JJ and STILL fears your QQ and thus doesnt reraise this river OR has KK and still reraises decreases the 2bet mistake to at least 1.95, which is fairly substantial when dealing with a breakeven situation.

These factors push a breakeven situation in to a favourable place to race for the max +ev.

Please, feel free to rebut but I think way too many people just saw a guy slow down to a Q then bet out a J without really considering the actions before. Expect to raise this and get called by KK way more than 60% of the time in the long run against an unknown