I think versus described V that his range is wide enough that he folds to a c/r some percentage of the time and that he won't always have an overpair. If V was OMC and his range is TT+ only then I play the hand a little differently. Sounds like he could have any PP, a lot of Jx/Tx, KQ, etc. Would hate to call here, find a brick turn, then V pots it and we end up folding. I want to see all the cards.

Hey OP, lot of info going around on this so far mostly about check raise or lead out...but I'll take a crack at this as well, although disclaimer I didn't fully read everyone's post before this....

If we lead out 1/2 to 3/4 pot: hands that may call us include, sets/2pair/AJ/QQ+/flush/Dry A of D. Now if he is aggressive the top half of his range may raise OTT, aka sets/flushes/dry A. However, you may fold out anything less than this. In the event he re-raise we must shove and assume we GII before cards come we hate aka no diamond no pair board.

If we check to induce check raise: If we assume only the same range bets as would call on previous example top of range will bet, bottom will check through, and I would imagine 2pr or sets will fold to check raise AI, of which you are likely to do. Check raising does have the advantage of getting stacks in before the river however most of those hands are raising YOUR bet OTT if you lead anyway, it seems to me check raising simple accomplishes the same except looks scarier and folds out hands you would love to raise you or at least flat the turn and fill up/get there.

I simply cannot find a range in this scenario that check raising gives you value that leading would not, especially the bottom range in question, if he's willing to bet AJ with no Diamond if checked to, then he's certainly willing to call half pot with it. And that's about the only hands I can see where leading isn't significantly better, as it gets the same money in and looks less strong.

Cliff notes: there are no hands that bet when checked to, that wouldn't call a bet, so just lead the turn and hope to see aggression/favorable river cards