somehow missed last time that you had position on him AND that he was the big blind. That makes a big difference. He may well be sitting there with something like AQ with the Ad, or something like KdJd. I think that once you call his check-raise you're committed to the hand, so you have to grit your teeth here and call.
Re-popping the flop might get him to fold something like TT (unlikely though). Flat-calling can go both ways - he may slow down and try to get a free river if he has the naked ace, or he may see you as weak and put the pressure on.
From a pot odds perspective you're being asked to call 305 to win 655
If he has a higher set then you've 1 out (1/44 chance)
If he has a made flush then you've 13 outs (13/44)
If he has a flush draw then he has 8 outs (i.e. 36 cards are good for you)
Given that there are 44 cards left and €655 to play for, you're looking at about €15 per card

Your equity against a higher set is about €15, against the made flush is €194 and against the draw is €536
You need the balance of him having each hand to be sufficiently heavy towards the draw to make €305.
If for example it was (5,65,30) then your equity would be about €280 - so falling a littler short
I'd say you need him to have the draw 35% or more to make the call worthwhile. Still just about a fold for me I think.