If you want to avoid being bluffed by your opponent, you can defend at the minimum defence frequency here.

Your opponent bet 0.18 into 0.13 here, so you need to defend 13/(13 + 18), or 42% of your range.

Assuming your opening range from MP is the following:

22+,A9s+,KJs+,QTs+,JTs,T9s,98s,87s,76s,65s,A9o+,KJo+,QJo

which is 224 combos. You need to defend 94 combos.

If you defend the following range:
22+,87s,76s,65s,AdKd,AsKs,AcKc,AdQd,AsQs,AcQc,AdJd,AsJs,AcJc,AdTd,AsTs,AcTc,Ad9d,As9s,Ac9c

which is all pairs, 87s, 76s, 65s, and all suited aces with backdoor flush draw, you get 95 combos.

So you don't need to defend AKo (it's right at the cusp). So, your fold is ok, theoretically speaking -- meaning that you won't be bluffed too much.

In general, most people actually under-bluff. And overbets are often value heavy. So you're often ok even if you over-fold.

C betting this spot is going to be more profitable than check/calling I would imagine. Capitalize on the fold equity/protection that betting provides. I get it, AK has SDV so why bluff? Look at how often you check or check/call this combo and get outdrawn on the turn by a hand that folds flop when you c bet and win uncontested. Look at the spots you missed where you could have protected/value bet thinly and won pots uncontested on the flop OR have a bigger pot when they make bad calls or you drill turn (preferably a K. There will be less 2 pair combos/straights on a K turn vs. an A turn).

I'd also fold. It's a reminder of being self aware of our range and xf frequency on the flop.

Checking range on this board is fine..If anything population will overstab against check because they extrapolate the way they play the game to how you will play your strategy, and population probably cbets too much oop against ip cold calling ranges, so once you check they'll perceive your range as weak because their range would be weak...so checking range as the pfr when oop versus an ip cold caller is probably a good exploit on many boards...as far as your x/c range here, i think this is fine, you have two overs against their middle pairs that might be overbetting for immediate protection, plus a gut shot that might should be good most often...also, they could just be sizing up with broadways that shut down once you call flop...also, one thing to keep in mind in this spot with regard to your ace high call downs, the larger the sizing the more you'll want to have the nut backdoor flush draws and overcards to their middle pairs to call, and the smaller the sizing the more you'll call all of your ace highs on flop...