Betting the flop/turn with a flush draw

I have aces preflop in mid position at 0.50/1 8 seater cash game and make it $5, i am called by the button. I have roughly $100 while my opponent has $140. Flop comes 10c5c4d i want to get paid but also do not wish to allow my opponent to hit the flush. What would you recommend betting the flop in this situation? My opponent called by the way with another diamond on the turn bringing a second flush draw, how would you also bet the turn? Thanks for your help

It depends on your opponent and how you want to play the hand on later streets. If you have been bettign flush draws a lot, it might be a good time to bet out and hard, in order to disguise your hand. We also get the added benefit of not letting our opponent draw for free. This is one reason why to bet your flush draws sometimes, so your opponents cannot put you on a made hand when you bet the flop with draws showing.

HU, it is very rarely right to check unless you plan on c/f if the flush fills on the turn. I like to bet the same amount here that I bet when I'm c-betting, so 3/4 pot.

I probably bet same amount to pot on the turn, or c/r against a very agressive opponent. The c/r is a good move if you think your opponent might want to steal the pot right there after calling your c-bet, but since your both deepish, hands that are drawing on the turn are more likely than already made ahnds at this point because of implied odds (excluding sets). A hand such as AK, AQ, KK, QQ, JJ or even TT might have reraised preflop. Suited connectors or big suited paint might not.

But since I'm a nit who detests giving away free cards for a little extra value, I bet out. Pretty standard.