Villain is a big winner. He's fairly loose and 3 bets me extremely liberally. I haven't done much about it as of yet.

How's my flop line?

I prefer a simple flop call here.

* I doubt that your opponent has a hand that you dominate (aside from a rare bluff), at best you are flipping with x, or x, at worst you are dominated by a good made hand like Q, made flush, etc. I don't think that your opponent will have a hand like T here. So by this move you will not make him fold a worse hand, and his big draws gain value by putting all the money in on the flop.

* By going AI you also your positional advantage.

* If you call, then you can bet a non diamond turn gaining value from his draws. You'll probably have a tough decision if he fires a blank turn again, but if you push over his bet on a blank turn, and your hand will do better against his range compared to pushing flop. (Simply put you'll lose the same to his made hands, but you'll win more from his draws.)

Oops. I've been away for some time, and I am a bit rusty now.
I missed your flop check there.

I agree that a shove is good to negate your positioanal disadvantage there. Still if you are ok playing for stack here, i.e. you think that your opponent range is quite wide I'd prefer a turn shove here. Though in your line with flop check stack sizes are not good for a turn bet. I'd rather see
A) flop bet/raise/call; turn open shove
or
B) flop bet/call; turn check/bet/CR AI.
Reasons for the turn bet are the same as in the previous post.