raise the flop as you have a very slight equity edge against his JJ+,AKo,AKs range which improves if you add AQs to his range but we can probably leave it out seen as its FR.
Equity Win Tie Loss Hand
Player 1: 52.365 % 51.001 % 2.727 % 46.271 % QhQd
Player 2: 47.635 % 46.271 % 2.727 % 51.001 % JJ+, AKs, AKo
It would be close between a cap and a call down after a 3bet, i guess it depends on how aggressive the opponent is and if he 3bets AK, if you think he would, cap and exploit your equity edge, if you dont think he will just call down as your equity against just JJ+ is about 36% which is easily enough.
After the ace comes i would probably fold although i think its close between continuing to calldown your equity is as follows;
Equity Win Tie Loss Hand
Player 1: 25.162 % 23.377 % 3.571 % 73.052 % QhQd
Player 2: 74.838 % 73.052 % 3.571 % 23.377 % JJ+, AKs, AKo
Im not sure of the formula for a calldown but i roughly figure you need about 16% for a call down here (if it was 3bet on the flop) which would suggest a calldown is profitable. Although this is hard to accuratly measure as your equity varies if AK is still in his range after the flop and if he would vary his play in face of the ace with JJ-KK
Phew! that got more complex than i thought.
PS. could someone analyse my analysis as its the first time ive done this type of thing so point it out if im going drastically wrong somewhere ♦
edit: i got so carried away and i forgot the 66% rule for raising , maybe its just a calldown from the flop no raise after all! Heck i dont even know any more why dont i leave it to a judge!