AK: Planned to go broke with 2P

I have 3bet him because Im OOP ...

but would be better just call, keep all the crap in his range and play a small pot OOP if called?

Grabbed by Holdem Manager
NL Holdem $0.02(BB) Replayer
SB ($1.20)
Hero ($2.15)
UTG ($2)
CO ($8.29)
BTN ($5.25)

Dealt to Hero A♥ T♣

fold, fold, BTN raises to $0.08, fold, Hero raises to $0.22, BTN calls $0.14

FLOP ($0.45) T♥ K♣ A♠

Hero bets $0.34, BTN calls $0.34

TURN ($1.13) T♥ K♣ A♠ 7♥

Hero bets $0.84, BTN calls $0.84

RIVER ($2.81) T♥ K♣ A♠ 7♥ 8♥

Hero bets $0.75 (AI), BTN calls $0.75

to be honest, I post this hand because Im not so sure if was the case to play differently here

maybe I can just c/c the river?
or maybe c/f the river?

villain is 79/53 with 83% of steal

so, doesn't necessary mean he got AK there but may be a flush close but my planned hand was to go broke by the river (by give a small change of flush in his range really almost hope for a worst Ace there) and I have tried to manipulate the pot threw the streets to allowed me to go broke on the river (any river at that point)

I still believe I got more to beat in his range than be beaten

Combonator Output combonator.com
Board: T K A
Vs Hero Cards: A T

Combinations in complete range: 256 [Hero Eq: 78.15%]

[b]  Grouped[/b]:  256 combos, 100.0% [Hero Eq: 78.15%]
[b]Ungrouped[/b]:    0 combos,   0.0% [Hero Eq: 0.0%]

  [b]Group 1[/b]:  229 combos, 89.5% (89.5% total) [Hero Eq: 85.70%]
  [b]Group 2[/b]:   27 combos, 10.5% (10.5% total) [Hero Eq: 14.10%]

[b]Group 1[/b]: Hand equal or worse than hero

QQ-JJ, 99-22, AQs-A2s, AQo-A2o, K7s+, KTo+, QTs-Q9s, QTo, J9s+,
JTo, T9s, 98s, 87s, 76s, 65s, 54s

[b]Group 2[/b]: Hand equal or better than hero

KK+, TT, AKs, AKo, QJs, QJo

ofc, as said I will not considerate now the possibility of flushes even if the % of that happening is relevantly high if I think more deeply

TY