Not many reads against villain, too loose pre flop

I felt lost on this hand as soon as I paired my medium ace on this 3betted pot. Maybe should I flat call to begin with?

His flop call, small turn bet and half size pot shove looked weird, but a thinking player realizing a have a weak ace or a mid pair would play the same. I nonetheless have 3 to 1 odds.

$0.1/$0.25 No Limit Holdem
5 players
Converted at weaktight.com

Stacks:
UTG Snack89 ($9.22)
CO kiliclimber ($46.73)
BTN Mr_GreenDK ($23.49)
SB zirookie ($27.04)
BB Hero ($35.39)

Pre-flop: ($0.35, 5 players) Hero is BB
2 folds, Mr_GreenDK raises to $1.25, 1 fold, Hero raises to $3, Mr_GreenDK calls $1.75

Flop: ($6.10, 2 players)
Hero bets $4, Mr_GreenDK calls $4

Turn: ($14.10, 2 players)
Hero checks, Mr_GreenDK bets $4.50, Hero calls $4.50

River: ($23.10, 2 players)
Hero checks, Mr_GreenDK goes all-in $11.99, Hero ?