With one overcard you need to make a proper C-bet. less than half pot is too small. Especially on this texture. He has a great price to call with Ad3s.
With 2 overcards depending on the opponent, I might just give up right there.
On this hand specifically, I bet ~0.20 on flop. Then check to him on the turn probably playing check-fold. He should be protecting Qx in that spot, and checking back any big diamond draw. He might decide to protect with 88/TT/Ad9x but those are the only hands you can beat and I dont like how JJ plays OOP on the river without the initiative. If he checks back, the river is close since the Kd got there. depends on his sizing for me there. On a river undercard that isnt a diamond, I'll almost always play check-call, unless he does somethign crazy.
Double barreling is also an option, somtimes he will fold his diamond draws. If he calls however, you are pretty much always having to play check-fold on the river anyway, and he might just decide to bluff you with Ad with no pair. You might consider playing check-call if you make your flush, but it's kinda spew if he bombs it.