In this specific scenario, I'd cbet 90% of the time.
You have zero info on your opponent. However...
You've already rep'd a decent BTN-1 hand by tripling the blinds. You're hand is better than a BTN-1 hand because it's 99, which is a 72% favourite in this scenario regardless. You're opponent may or may not think that you're late position allowed you to raise with a wider range of hands, so let's assume the worst, let's assume the BTN is smart and aware of your position advantage on the previous hands and would be willing to call with a wider range as well. .... another look at their stack tells
us that they won't be in with low pockets or low suited connectors because they don't have enough money to get the implied odds
they'd like. That leaves an average player with a range of Ace-BRDWY(s or o), BRDWY-BRDWY(s or o), suited connectors equal to or greater than 67 and pocket 99's or higher. That'd be my initial preflop range and I'd stick to it based on having zero previous info.
You're highly likely to be winning here with this board. Your opp is 32% likely to hit a pair, very unlikely to have hit the straight draw here so I wouldn't even consider it(yet). Odds of your opponent having two hearts are even smaller since suited cards only flop a draw 1 in 9 times.
Here I'd bet 3/4 of the pot to protect against a flush and give myself good value if they're chasing a flush or straight draw. If they came in with one of those middling connectors like 7-8 or 6-7, they may just fold, but here you have to hope they call because you want that cash and their odds of beating you aren't worth paying 3/4 the pot. ESPECIALLY since you have two of their straight outs to prevent any crazy runner runner cards from hitting.
The only time I wouldn't cbet this is if I was against a really LAG player who I could check raise this flop. A player I know would bet any two cards regardless of the flop. Id even cbet a calling station here because it's just too likely that you're ahead already.
Now, had you done this with say [K-anything(s) or worse] and missed the flop, there are a few more scenarios that a check would be appropriate. Against a calling station, you check. Against a flush and straight making board you check. Against a super low vpip you check.
I'd say here, even if you have A-anything that misses against a calling station, you get ready to fire two barrels because the odds simply say that you are likely winning with Ace high and most calling stations go away on the turn if there isn't a straight or flush to be had.
long answer... but that's how I'd play that hand.
Personally, if I'm the PFR and I get in heads up, i'll cbet against almost any board and any player. The only times I don't are against calling stations, double scare boards, and LAGs(I will check raise these mofos sometimes). Otherwise, I fire away and am often ready to fire the second barrel when I know my opponent is the type that folds the flop or turn often.