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Since we aren't folding is there any value to 3 betting for a free showdown unless we improve on the river? Will we really be 4 bet even by aces? Also we'd be happy if he folds a 6 outer.

-DeathDonkey

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This is a very good point. Generally, if we put our opponent on a bluff the last thing we want to do is raise, but in this case a bluff is very likely to have 6 outs, and if you reraised the turn you could make the villain incorrectly fold this 6 outer even though he has the pot odds to call(this would be wonderful)
But heres the problem I have with this line in this particular situation, Since the villain already has the aggressive initiative in this hand, If he was going to bluff he would simply continue his aggressiveness by betting the turn, especially since the hero has showed no strength in this hand so far and could be folding the turn to a bet for all the villain knows. So I think the probability that the villain is checkraising as a bluff is very low. The texture of the board also supports this given that there is no flushdraw possible thus eliminating many semibluffing hands. So getting approx 7.5-1, I would just call and not 3 bet for a free showdown becuz I think the probabilty of the villain bluffing is too low which also means the chance that the villain will 4 bet goes up, so i would rather cheaply call with my six possible outs, and if i dont improve on the river, Im gonna call partly becuz I wanna show him that hes not gonna run me over and also becuz theres always a chance my read is wrong and the villain was bluffing after all.