HERO($8.78) is SB
Villian($5.61) is BB

HERO has AKcc, raises to .15
BB raises to .50
HERO calls .50
(pot 1.00)

Im unsure whats better, flatting or re-raising when BB raises our open here. We're not relatively deep and are at top of our range so does that warrant a re-raise w plan to play for stacks? Stack sizes here make it hard to 4b unless we're shoving. Tough when we 4b to $2 and then brick flop and villian only has pot size bet behind. These spots are tough for me to navigate. What do you guys think?

FLOP: 4s 4c 6c
HERO checks
BB bets .65
HERO calls .65
(pot 2.01)

Idk if flatting or raising here is most profitable play? Our hand has a lot of value w NFD as well as 2 overs. There will be a decent amount of time that our AK is best hand on this flop. Is there any merit in shoving here w villian having ~$4.45 behind? Our implied odds might not be great for our hand if BB isnt barreling on turns that give us best hand - if/when the ace peels on turn or club if hes checking behind then i think getting all the money in on the flop is best? Im unclear if this logic is right so any opinions/insight are welcomed

TURN: As
HERO checks
BB bets 1.75
HERO calls 1.75
(pot 5.51)

I think flatting the turn is a glaring mistake on my part. When he bets $1.75 he only has $2.71 behind so we should always be getting the money in right? By checking we allow him to check behind on the river and get to showdown w all of his aces, which he will have a lot of in his range when he double barrels after A rolling off on turn. I think flatting here costs us a lot of value to be had. Is this on the right track?

RIVER: Tc
HERO checks
BB checks

I think the river checking through puts in perspective why we need to be playing for stakes when villian bets turn. In this particular hand it might not have worked considering what villian has, but most of the time when villian double barrels 33% of remaining stack on turn when A hits, hes gonna have value. I think overall we costed ourselves his stack in this hand. What do you guys think? Im still unsure at what point is the right one to put in the raise - pre flop? Or turn? I think flatting the flop is okay since it protects our hand when he has pocket pairs that we arent ahead of yet.

SB shows AKCC, wins 5.51. BB shows 78dd