Standard(ish) marginal BvB spot, all lines seem meh

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Standard(ish) marginal BvB spot, all lines seem meh

BN: $102.66
SB: $100 (Hero)
BB: $141.98
UTG: $210.56
HJ: $181.83
CO: $100
Preflop ($1.50) (6 Players)
Hero was dealt 2 A A 6
UTG folds, HJ folds, CO folds, BN folds, Hero raises to $3, BB calls $2
Flop ($6.50) 5 4 K (2 Players)
Hero bets $4, BB calls $4
Turn ($14.50) 5 4 K T (2 Players)
Hero bets $11.50, BB calls $11.50
River ($37.50) 5 4 K T 2 (2 Players)
Hero checks, BB bets $30, Hero calls $30
Final Pot
BB has 6 T 3 A BB wins $94.20

Villain is a 24/16 reg, more to the aggro side, but nothing that stands out.

Now I am not really wondering about this particular river spot so much as I think its very close without better reads (but definately comment on it if you like), but as I am thinking more about the hand, it seems to me, that whatever line I choose postflop, it always sux.

The line I chose: Bet, bet, check/decide leaves me guessing (or easy folding) on pretty much every river except: A and 3 + maybe T, 5, 4. And even on the best of those its never a clear valuebet and when check/calling I am almost always bluffcatching.

Bet, check/call, check/decide line: seems maybe a little better in hindsight, because he will have a little tougher time deciding what rivers to bluff. But otherwise its the same, I dont like pretty much any river. And also by checking turn I lose the chance of possibly making him fold a hand with equity (like I dunno, A976ss, 9864r, ...)

Check/call(or maybe fold to very strong bet), check/decide, check/decide. I didnt really think of this at first, but it actually seems viable as I can happily continue on quite a few turns: Aces, spades, Threes, probably Fours and Fives (around 19 cards out of 41, so 46%).

Check/fold flop. Seems too weak, but it prevents me from getting into spots where I often can make a mistake. Still dont like it with a hand this strong, but dunno.

...

So basically the question is:

What are the factors that should influence which of the above lines to take with marginal hands like these? Like what hand is a bet-bet-check/decide here, what hand is a bet-check/call-check/decide and what hand is check/call-check/decide-check/decide? I am curious what nuances you guys are looking for and where you draw the line between hands.


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