[melioris]

I think it is fine to call preflop. You got position, why negate all that with a push preflop? Calling the flop c/r is tough, IMO. I like a fold here 75%. I think at best you are calling for a chop.

Answering your question, here is my thought process on this hand.
Preflop
“SB is raising my BB and I wake up with AKs, 3-bet biatch!”
“WTF that cheeky bastard. Mini-4 betting me. So you weren’t just trying to steal and have a hand. Rough range 99-AA, AJ+, but with the mini 4-bet, donkeyspeak for I want to induce a shove by you as I have a monster so maybe his range is smaller, I’ll just call with position and check out the flop.”

Flop
“Boom, and you check. Ok, no FD out there, and I don’t want to bloat the pot so I will check behind and let you led out the turn.”

Turn
“Yep, you are betting with your entire range here so calling is +EV for me.”

River
“I can call just about any reasonable bet here and check behind in this 100BB pot to avoid a crai.

As played-

Flop-
“Ok, I got TPTK and you are checking to me. I’ll bet.”
“Yuck, crai. I am ahead of AJ and behind everything else except a chop. Now, do I think he does this with KK, JJ, TT or 99? If not sure, fold. If yes, call. Yes it is a desperate CRAI overbet, what does that mean? To me it means I hate it when I get into these situations.”