I think on AT4 two tone specifically most players in your situation will not have a substantial c/r range as the PFR. It's just not a spot where weak made hands are very compelled to bet when checked to. For example anything made hand strength like A8 and lower is likely to check back, whereas on J34, theses low to medium strength hands have greater vulnerability and gain more from getting protection. So frankly, I don't really buy that you could have many sets here and I'd be surprised if you could ever have a flush.
On the river, you have a few things going against you:
1) You're unable to check-raise here to a small enough size that would give you reasonable pot odds for your bluff (i.e. to 23.82, which would still require him to fold a whopping 50%), because it would likely be too small to fold out any non bluff hand in practice. You end up risking nearly 2x what is in the pot so he has to fold nearly two thirds.
2) As above, your actual range notwithstanding, an extremely narrow slice of your perceived range could be taking this line for value. I think you credibly rep 55 and 7h6h/7s6s/7d6d, and that's about all.
3) I think his range to bet 9 on the river is pretty damn strong to be honest. Imagine what his flop check back range looks like and how few of those hands are strong enough to bet river, especially if he's the type of player who is wary of betting a capped range in position. A lot of regs will pass on fairly thick value bets in such spots just because they don't want to be check raised. He probably can't have a big ace, and he's potentially not value betting A7. Essentially, he's either bluffing or he has aces up or a turned or rivered set quite often here. I'm a little bit afraid that for the pot odds you're laying yourself that he only needs to defend A8+ to be snapping you off plenty here. I'm curious what your thoughts are here, maybe I'm seeing monsters under the bed. If I'm right, this is pretty devastating to the viability of your line.
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