Check raising is bad because he is never folding anything better than your hand with like 50 cents behind or whatever it is. If he is super lose passive I just bet/fold all 3 streets big enough to get his stack by the river. As played I fold the river.

Yes, definitely no point check raising because his range is pretty polarized to full houses and bluffs, in which case he calls when he has you crushed and folds air. He can be value betting a 4 that didn't fill up (may even check this back) but then you wouldn't be check raising as a bluff here, you would be value raising, and he might end up folding that, which is bad.

Your hand looks like a sticky AAxx OP type hand so I like the way you played it because you narrow your perceived range and keep his range wide and keep in his bluffs. When you double barrel I think you narrow his range too much in a spot where you can be crushed too often when called.

The issue I have with his bluff range is that there aren't a whole lot of combos that he will float the flop with and turn into a bluff, assuming he isn't bluffy in general, stats here would help a lot. I guess he could have the nut flush draw and over pairs himself but otherwise it's a dry spot to be floating in.

Check folding is ok I think against very tight opponents that you are pretty sure will check back a 4. But in saying that it leads me to want to bet fold the river against these players to avoid the negative freeroll. I'd be check calling against more aggressive opponents.