AA, What's the best play here on turn based on SPR? 50NL

Villain is 56/12/3 over 80 hands. His been limp calling a lot and usually giving up on flop and turn bets. His minraise then calling a 3bet range from button is pretty wide.

PokerStars No-Limit Hold'em, $0.50 BB (5 handed) -

Button ($34.25)
Hero (SB) ($54.20)
BB ($51.95)
UTG ($108.85)
MP ($61.15)

Preflop: Hero is SB with ,
2 folds, Button raises to $1, Hero raises to $3.50, 1 fold, Button calls $2.50

Flop: ($7.50) , , (2 players)
Hero bets $5, Button calls $5

Turn: ($17.50) (2 players)

On the turn, against 100BB effective stacks I would bet out around 12 and reevaluate on river. But if I bet out 12 here, I don't see me check folding to a $14 bet on the river. Wanted to know other's thoughts here on the best course of action. If I'm not gonna fold to rest of his stack if my $12 gets called, is it better just to shove on turn? Or betting $12 and then betting $14 no matter what the river is a better option? What about C/C, C/C?

As played bet turn, bet river.
Potting flop and then shoving turn for about pot is an alternative line.