I recently had a villain take a similar line that was strange to me at the time and similar to this. Small bet, small bet, small bet. He ended up showing TPGK and I won with TP better kicker.
Point being, it was a made hand but not a monster, which in the context of this hand would be QQ/TT, add the tilt factor and maybe 7x SC's and A7s are in range here. I would think that Jx would be going bigger OTT. AA should also be going bigger OTT, but the tilt factor might be making his bet sizing screwy.
I think this feels like KK is good here most of the time. My range for villain is QQ, TT, A7s, T9s, 89s, 87s, 76s. For the sake of balance, I'll add in AA. With this range, we have 77.5% equity and then we should raise to try to GII OTR. I like a min-raise here. My thinking is a shove only gets called by better. A min raise gets called by worse and makes river shoves difficult for villain to fold to when they are tilting. (Plus min-raises against tilted players drives them crazy and is entertainment in itself. I'm recreational, deal with it.
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If we add AJs,KJs, QJs, and JTs (and JJ) our equity drops to 63.7%. A min-raise will induce these hands to shove OTT, no? We can fold exploitatively, no? Will villain, donk lead twice and then jam to a raise with worse hands here?
I'm very open to the idea that the above is stupid, just wondering what you think about it.
EDIT: Read through the thread and found you were thinking raising small as well. Question stands.