for starters, i think your flop bet is way too small. i dont think he's folding any of 88-QQ on this board to a 3/4 or greater bet on the flop. plus he can have AsQs AsJs perhaps. we're only realistically afraid of AA which gets 4bet preflop like 70% (estimate) of the time by villains at 25nl = he doesnt have AA as much as he has 88-QQ.
had you made it $8-$9 on the flop and he called, the pot would be 26-28ish, villain would have $13-14 behind AND we pretty much crush his range. he very rarely has 44 or 55 simply because there are so few possible ways to make those hands out of the cards left in the deck. betting larger allows villain to misplay his hand, as your range is far stronger than his. as played you cant c/c the turn and not call a shove on the river. i probably check/shove the turn. allow your hand to turn face up and let him try to rep the ace. if he has AK here (i think this is unlikely), then bad luck. sure he played the flop bad, but you could have allowed him to play it a whole lot worse by betting more.