Beginner preflop question

I never play online and generally play live with $2/$5 blinds so I'll multiply by 100 and give this a try. With fairly weak aces (the king doesn't help as much as some think) playing moderately deep I don't like to three bet out of position since the likely result is something ugly (set mining with an SPR of about 4). In position maybe I'd three bet an opponent I have control over.

Given you three bet and ended up against one opponent (which is rare in live play *) with this flop containing two hearts but otherwise moderately dry I'd lead about half pot given I have the ace of hearts. I'd be done with the hand if raised and reevaluate turn if called (possible bluffing a heart). . Since you checked I'd fold to this bet as you have very little chance to improve in a way you would be confident getting it in.

* A lot of the advice online and on training sites (outside of this forum) concentrates on online 6-max play. There you get heads up a lot. In my games it's usually eight players seated and most flops are four to six ways with a single raise about half the time and a three bet rarely (almost always indicating decent aces). I might be heads up on the flop no more than once a seven hour session so take my advice with a big grain of salt!

At a decent frequency I’m betting 2/3 on flop and blasting off on hearts. I think our hand could go for a check raise since we do block some continues with the 8 and Ah.

PLO Matrix has this as a raise/reraise.

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Flat pre. Unless specific reads on opener. Don't build a big pot out of position where you're not going to hit very often. You're certainly not playing this to 'set mine', you wouldn't /shouldn't even be doing anything near that in live poker either. But you do want to have good board coverage, and this has only slightly more board coverage than AAA7r. AAA7s is a better hand (fight me if not) than this.

On the flop, you need to consider two cards in your hand: the ace of hearts, and the 8. When you have aces, with the blocker but not the draw, this is license to bet the flop, as it weakens their range as well as gives you the possibility to barrel when it hits (more difficult to rep when you check the flop, and less big of a pot to steal). The 8 blocks his straight draws; all-in that means that when you're divvying up your range of [AAxx that we're not willing to at least bet-call the flop] and choose which we're c-betting and which we're checking, this is a far better candidate to bet than check.

The lack of co-ordination of the flop also makes it a good candidate to bet. A KJ8 board also has no straight possible, but it should be clear that even amongst loose players, that board smashes their range for two pair, whereas this doesn't.

Having the A hearts also means that his range for raising our flop bet is stronger as that's a main constituent of his drawing range. Which gives us a slightly easier fold.

Don't worry too much about getting floated and finding turns difficult to play, or not having confidence in a triple barrel on a flush turn getting through. The flop cbet will show more than enough profit on its own and villains don't float or draw very well at every level, so you won't be punished too hard. If you never triple barrel the nut flush blocker at these stakes, I doubt you're leaving too much money on the table.

PLO Matrix has played billions as many hands as you have and is... you know.... very good at poker. It's also perfecting its algorithms against itself. It would be a mistake to apply a solver strategy without understanding it to the bones. This is a perfect example.