Tough one. Don't have to worry about him having very much Ax, so yeah I guess you would be trying to get a call from something like he has, some Jx. I guess you could bet small to get called by something like that, but yes it allows him the opportunity to bluff you in that spot. I am at lower stakes and have found on MPN, my smaller bets like 1/3 pot or thereabouts, seem to get raised more frequently, so you could just be opening yourself up to get raised a ton. Not sure really. I think I would probably check back but I think that is a leak of mine as well. I don't go for thin value enough. Not sure if this spot qualifies. I guess it would depend on villain, but because it is anon, you don't have stats to go on, just table reads

Now when i look this it is a value bet, because my hand is going to look like AJ+ or notining, in his shoes it looks like i have to check back QQ,KK and he block AJ and some weird AK.

But real question is what you guys think about check jam in his shoes, JK block AJ, and what should be my raise call range, AJ+ or wider?

So yeah I think I agree with you. I did a pretty quick and dirty calldown. I think it would depend on villain and how he constructed his ranges. The way I did it, KK actually had enough equity to value bet the river. On my calldown I had no Ax for BB on the river. He would have had to call 2 streets with A high, and I just didn't think he would. As it was BB had 76, as you suspected, as a bluff raise on the river. 76 makes a decent bluff raise as it blocks 77 and 65. At first I thought KJ wouldn't be a good bluff, but against your value range it doesn't have much equity. I thought it would be too strong. However I guess it might be a good candidate to turn into a bluff raise as it blocks JJ, AJ and KK.

Against a pot size raise, I think you would have to bluffcatch with AJ, maybe even AA, which would be decent as it blocks AJ pretty hard, one of his main value hands. All this is assuming he gets to the river with 65, 77 and 44 and hasn't raised them sooner, which I am not so sure about. Against a jam, I don't think you would have to defend all your AJ.

I didn't go in depth with it all, but kind of looks like KK would be a bet/fold on the river, especially if you thought he was bluffing mostly with KJ. You block KJ pretty hard with KK.