based on your reads, he bets this turn
doesn't bet:
88 - 6
99 - 6
total 12

does bet
TT - 6
JJ - 6
KQs -3
AQ - 6
total: 21

21/33 = 63% of the time. and probably stacks off incorrectly with {KQs,AQ} = 9/21 = 48%. so i think check/shove is a great way to exploit him caling flops/betting turns light (ie his turn betting range is likely wider than his calling range). may also end up getting it in vs the BB's QJ/KQ/AQor something. your hand is considerably stronger than both your opponents ranges. and it seems they're both going to be more willing to put $$ in the pot if you check the turn instead of betting it.

all of the above assumes the LP villains folds hands weaker than KQ when you bet the turn. which is likely if he perceives your turn barreling range as strong.