Will you ever check a better hand on the turn than this AQ? If not you will fold 100% of your range which is something you never want to do.

With no reads on the player I will never go this far off from GTO and fold 100% of my range.

Ok firstly I'd just say stick to at least 3x preflop. No reason to go 2.5x from MP.

I'm going to go through what I feel firstly. What hands beat us? AA, TT, AT, AK. 33. On the flop.

33 seems unlikely they choose to 3bet. TT I think many just flat, but sometimes possible. ATs... could be possibly squeezing.

Really I just expect the guy to cbet all his AK, TT. TT want's value from Ax and some fds etc. AK just wants value vs your type hands and fds, JJ, QQ etc.

Mainly this pot was multiway on the flop and he decided to NOT value bet/protect his hand or raise when you bet with the flop with a person left to act... what does that say?

As played, any draw missed (such as KdQd) and this just doesn't make a lot of sense. In this spot have to make the call and make a note.
I am however legitimately confused as to what opponent has. The only hands that makes sense for value is AA or ATs which he could play this way. But I can't see me folding tbh.

One thing I'd add is, if you went bet, bet and then the guy still did this I would more often lean towards a fold

When you take this line, I think opponent makes a decent bet for value hands on river, or jams bluffs.

If opponent took this line for value then I just think it's miss-played, but might work vs me.

Actually I add something, like an edit. If I bet, bet after the guy plays this way then I don't actually think I can fold as we would be committed. So I correct myself from previous post.

Pre: Seems fine to me.

Flop: In a three handed pot here I do like betting when the original raiser checks to us. I like your sizing also.

Turn: I would probably bet once more then look to check back rivers here.

River: As played I don't see myself folding here. It's hard to see what villain has for value that plays this way that isn't exactly AA IMO as other sets should be betting flop. I won't be shocked if we are behind but I'm not folding.

Simply betting the turn prevents you from making a mistake on the river like this. We can get value from worse Ax and JJ-KK.

If we bet turn and he ships then I would give him credit and fold.

As played I think I would also fold the river but I'm really not happy about it so would avoid the situation to begin with by taking a standard line of betting twice and folding to any raise. Being in position is a huge bonus when you're holding a two streets of value hand like this.