In preflop, villain catches your opening as a standard.
If we choose a smaller aperture size, possibly our range would be perceived as wider. But since we are OOP, our value range is most likely very strong. So if we want to have hidden value hands in our range, it is a very good size to consider preflop.
The flop is quite dry, so we can check a sometimes in these spots. Another option could be to make a small cbet. And another option is to make a size larger than half the pot, to definitely polarize ourselves. This last alternative can be applied better when playing with wide ranges as in this case, BvB.
The turn is a street that favors range V more than ours. New flush draw combos are opening, and we could bet for the protection of our values. As played we hope to induce bets to bombard with our best bluffs.
On the river the problem with checking is that our passive line is not very credible. The reason is that we represent the best flush draws (obviously villain knows that's not possible, because he has his semi nuts). So we are inducing the villain to check a high percentage of the time, when he does not complete his flush.
As we have played the turn, we should now hope that any loose blocker V has (Ad; Kd) can fold and make our bluffs profitable, for example with AK without diamonds.
And if he pays us with the majority of his range (we are only defeated by a combo of 4), part of his calling range could become a
bluff, so we could make a neutral bet to induce that bluff or that V can to pay with hands that are marginal for this texture. For example: K9; TT; etc.
Greetings.