one hand we didn't talk about popped out of my memory from our last session

and I thought it would be an interesting one to share with the other players

it happened before you came and involved one dude that left the table early

here's the situation

I'll explain the situation and what happened, and ask some questions after it

5-5 game

stacks :

UTG about 225-230$
me in middle-late position, I cover him

UTG raises to 25$
I got AQo in middle-late, I make it 80$
back to him, and he calls
flop comes A-J-J
he checks, I bet 125$ and he folds QQ face up

questions are :

considering his stack size, making it 80$ is a good sized raise ? or should I consider only flat calling because it makes me quite commited to call a shove since it would cost me about 150 to win more than 320

would you consider checking back this flop ?
after the hand I thought I could have choose to do that and might induce a bluff from him on turn if he tries to scare me off with the A...
and if I bet the flop and he goes all-in, I'm calling anyways if he holds AK or a J or AT-, so it's about the same result if I check back, because if he holds this hand he would the turn anyways... but checking back the flop gives him the option to try to make a hero shove and push me out of KK or QQ or TT 99 etc..

let me know how you would have played that situation, flop play kinda bugs me