Not sure about check/shove because
1) CO may like to float heads up but the fact that sticky BB is there makes the play much trickier, so he may well choose to check behind instead (even if he bets JJ, JJ and Qx are only 15 out of his 39 combos (discounted KK))
2) CO bets $5.8, BB calls $5.8 (maybe with A6s a Q or FD or FH), Hero shoves, CO folds most of the time - unless he thinks you are fos AND BB doesn't have much - or calls with an unlikely better hand, BB probably folds worse and calls better apart maybe AQ.
So bet?
May I ask you about your rationale for your bet sizing on the flop? (I am not questioning it, just asking). In this kind of situations I would tend to bet something like $2.2 if not more. I also don't cbet without a hand, I don't know about you, but the fact you bet even though you are sandwiched vs 2 may also make the CO think that you don't have much air in your range, and make him less likely to float with stuff like underpairs?
edit: combo count
doesn't bet:
77 6
88 6
99 6
TT 6
total 24
bet:
KQs 3
AQ 6
JJ 6
total 15
So he bets only 38% of the time.
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