You've got a lot of good thought processes going on here, I like that you have a plan.
Bet the turn or check back the turn.....both can be OK if you have good reasons and a plan.
Check back the turn: benefits: controls pot size for the times you are beat. under-reps your hand to earn you more chips on the river. induces bluffs. also induces worse
hands to think their hand is good.
drawbacks: obviously they can draw out on you. also, you'll lose value from 2nd best hands like JJ.
Ideal against: aggressive tricky or bluffy opponents. also, chronic donk bettors who are likely to still have nothing on the turn and will give up if you bet the turn. these types of players are either drawing dead, or drawing to 2-5 outs and so giving them free cards is no big deal.
bet the turn (something like 35-50% of the pot)
benefits: a classic value bet that you are hoping will get called by a worse hand. protects your hand against draws and random 2 pair combos. gives cover to your future 2 barrel bluffs.
drawbacks: may be too much pressure for 1 pair hands like A7 to call, so more likely to get called by hands that have you crushed already. Betting on the smaller side will keep in villain's weaker hands, but also offers attractive
odds to any draws.
Ideal against: calling stations. any players who overvalue top pair. players you have recently caught you
bluffing, or suspect you are bluffing. anyone you suspect is on a draw.
Now here is my question for you: Why do you think 3x raising his flop bet is the best play? I'm not saying it's bad, but I want to understand your thought process. It seems to me that it makes it very easy for his weak hands to fold and will usually only get called by hands that either crush you, or have good
equity against you, such as 2 pair, sets or 1 pair with a gutshot.
Sometimes I think people raise the flop with hands like AA and KK in spots like this because they're afraid and they actually just want the other players to fold hands that have little equity rather than risk the small chance of getting their Aces cracked...that is the WRONG reason to raise the flop. Can't be scared of your own shadow with your premium pairs on relatively safe boards. If you were to tell me it was because you put the donk bettor on a hand like 88-JJ and it was a value bet, I would say "wow, excellent read and good thought process" or if you were to tell me you wanted to get heads up because AA is easier to play heads up I'd say "Ok, that is a fair reason still slightly on the scaredy-cat side on such a safe board....but still basically OK".