Flop Cbet is fine depending on his flop continuing range. Does he call with 2 over cards? 

Why exactly did  you check turn? It seems like you are giving him a free card there. And with the straight and flush draw, it's better to bet turn. Hoping to get called or raised by his gutshot/draw. Even a worst J. 

But you kinda have to make sure he never flat calls QQ KK AA. 

As played, I don't think I could fold that river, given his stats. 

But it also depends on what levels he plays. Does he see the 9 as a good bluff card because he thinks you are a level 1 thinker that will believe the 9 helps him?

Or does he think the 9 will make you think it's unlikely he has a 9?

I would say it's a flat preflop.  No reason to raise really oop.   We can trap up our villain on a bunch of good flops for us by he's a fish and expects people always 3 bet big hands.  This has just seemed to work for me lately be your range is so wide that you can take villain to value town when you flop big and they will never see it coming.

Just my opinion. 

I think preflop can be fine, especially with a little bit of gameflow. It's not uncommon for these sort of opponents to call a 3-bet oop w/ a suited Ax, KJ and so on. 

Could you elaborate on the BB please? General stats and thoughts about him would be helpful.

I dislike cbetting the flop, in my opinion people who would flat AK pre, don't fold it on a 9-high board. They may be even calling AQ and certainly are not folding any pairs. I think your idea of BBs coldcalling range is acurate, that being said I think you sort of fall into a cbetting auto-pilot OTF because said range has you crushed on this board.

It seems like you are giving him a free card there. And with the
straight and flush draw, it's better to bet turn. Hoping to get called
or raised by his gutshot/draw.

I do not think that it matters that we are giving villain freecards, his range is so small preflop that FDs and straight-draws will make up a tiny part of villains range. I must be honest, I am not sure what the best play is. This sounds weak, but I really want to check-fold. I think he has a really narrow bluffing frequency when he bets. I think his overall betting frequency in this spot is really thin, like QQ+. AJ has to be discounted because we do not really know how often he is x-folding that hand OTF and other than a bad valuebet with Jdxd I do not see what we would beat. 78 is really speculative, I doubt that he would flat that with a 100% frequency preflop. 

Betting the turn might be intresting against really bad recreational players who flat something like A6s or 77 preflop and are just too stubborn to fold, but here again we would need clear infos about the player and we do not have those. Details matter a lot here, for example, is villain overplaying hands and would bet something like 98 on the turn? Would he randomly call T7s in the BB because he is bored? Then suddenly this can be very quickly become a profitable x-call on the turn.

I like pre. Unless UTG is crazy aggressive I think 3betting makes it a little easier to get the money in.

On the flop I still prefer cbetting. It's not ideal because we're OOP to two players one of which has a narrow range (actually not that narrow since he should be coldcalling wider because of UTG) and we prolly won't get that many folds. However we still have a lot of cards to continue barreling on and a very good scenario if we get to isolate UTG.

Unless you're planning on c/shoving the turn, I prefer to bet myself because he'll most likely check back TT, 9x, doesn't have many bluffs in his range and is likely to take a freecard with his draws.

I think you messed up your betsizing a little bit though. 3way you should either cbet the flop closer to 1/3 pot and play three streets or cbet 2/3 and play two. Given that I'd want to induce light flop peels especially from UTG to later on maximize my FE on decent barrel cards, I'd have bet around 1/3p and 1/2p on the turn. Then I'd happily c/f the river vs the BB and expect to win vs worse pairs a lot (the smaller betsizes make it even more likely that he calls the turn again).

What are BB stats?