I like leading the flop, too. I think it's too much to assume your pair of aces is no good and betting maximizes value when they are good and minimizes loss when they aren't. Obviously, you aren't going to fold to a raise. But what if you take the check/call line? Are you check/folding the turn? That wouldn't make sense to me. In fact, if you take the passive line, I think you're pretty much committed to calling all three streets for one bet. The only reason I'd like a check on the flop is it gives you a chance to get away if there's a bet and a raise or worse behind you.
As stated by others, the turn is an absolute must call situation.
Just to clear up a couple points about the draw on the turn:
1) You only need 4:1 to call with a flush draw on the turn. You'll win with the flush about 20% of the time. So you win 4 20% of the time and lose 1 80% of the time. These two values are equal.
2) The board paired on the turn. I think it's a safe bet to say that someone has at least trips, so a river ten probably won't give you the best hand. Plus, it's possible that you're drawing dead or you will river a flush as someone else rivers a full house. I wouldn't consider this a full flush
draw. I would cut your chances to at most seven outs to compensate. You need about 6:1 pot odds
now, which you have so the call is still ok.
3) You have some implied odds and some reverse implied odds on the river. If you hit a flush and it's the best hand, I would expect to win at least one extra bet on the river. On the other hand, you may hit a flush against a full house or quads and lose two bets on the river. I think you still come out slightly ahead on river bets, but not by much.