NL200 Value bet this river?

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NL200 Value bet this river?

BN: $566.72 (Hero)
SB: $240.89
BB: $212.31
UTG: $1028.37
HJ: $247.26
CO: $254.14
Everyone's a reg here.
Preflop ($3.00) (6 Players)
Hero was dealt Q J
UTG folds, HJ folds, CO raises to $5, Hero raises to $15, SB folds, BB calls $13, CO calls $10
I wanted to play HU with CO who I think will flat a lot of 3-bets and at the same time prevent myself from being squeezed by one of the blinds.
Flop ($46.00) T T A (3 Players)
BB checks, CO checks, Hero bets $14, BB calls $14, CO calls $14
Decided to bet small here as kind of a cheap semi-bluff. I may bet this amount with Ax/Tx too since it's a pretty inelastic board.
Turn ($88.00) T T A K (3 Players)
BB checks, CO checks, Hero bets $35, BB calls $35, CO folds
I want to keep weaker Ax in the hand, and Tx is obviously not folding, so I bet small again for value.
River ($158.00) T T A K Q (2 Players)
BB checks
BB has $148 behind

I think shoving river looks really strong and I might only get called by boats at that point (AT, KT, QT).

I could bet a smaller sizing and hope to get called by Ax hoping for a chop or Tx as well.

BB's range that I beat (or chop): T9s-JTs (4 combos), AQ (6 combos), AJ (6 combos), Axcc (maybe 1-2 combos)
BB's range that beats me: TT (1 combo), QTs-KTs (4 combos)

What bet sizing should I use here (if any) and how can I balance this?

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