FR 2NLHE

MP2: Hero
UTG: Villain

Villain stats: VPIP: 28 / PFR: 14 / 3BET: 0 (Hands: 173)

UTG raises to 3bb
Folds to Hero
Hero raises to 9bb with AKo
UTG calls

Heads-up
Flop (19,5bb): 2s 5h 7c
Villain checks
Hero bets 9,5bb
Villain folds

So before I try to calculate if this Cbet was +EV I assume that Villain has a opening range from UTG of about ~8% which is to loose I think but it would match to somebody with a VPIP of 26.
So his 8% range would be: 77+, ATs+, KTs+, QJs, AQo+
So I think that are about 82 combinations:
77+ (6*6 + 2*3 = 42)
AKo = 9
AQo = 12
AJs = 3
ATs = 3
KQs = 3
KJs = 3
KTs = 3
QJ = 4

But because Villain doesn't raise I exclude AA and KK (- 6 combinations)
And he doesn't fold, so I exclude 77 and 88 (- 12 combinations)
So his range when he calls consits of 64 Combinations.

Then on the Flop (2s 5h 7c) I think he is calling with 99/TT/JJ/QQ would he also call with AKo? I don't know so I just expect he is calling with his overpairs.

That means he is calling with 24 (99/TT/JJ/QQ) combinations and folding with 40 combinations.
Thus he is folding: (40/64) of the time which is 0,625 so about 60% of the time.

And because I am betting about half the pot, I just need him to fold about 32% of the time (9,5/29).
So I my assumptions are correct it was a profitable cbet bluff.

Please let me know where I am wrong.