oh really tough spot. first of all i guess either cbet or checkbehind have their pros and cons in that spot
cbet -> you take down the pot often with qhigh and you can also 2nd barrel if he just calls. problem is -> what to do you when you get checkraised
checkbehind -> theres no chance of a checkraise and you can also take down the pot with a delayed cbet on turn. or you advance to straight or toppair.
so i guess both things are possible here.
the thing now is do we have enough equity to make an allin here (without any foldequity)
we need about 35% equity here
thats without the all the heartdraws... so its not really correct! but you should easily have >35% for sure! so going broke
Simulated 100000 Holdem Hands (Monte Carlo)
Simulation by Slice - The ev++ Equity Calculator
Player Equity Win Hi Tie Hi Range
1 44.2 41.3 5.7 77-99, A"T-9"{RB}, [K]T, Q"J-T"{RB}, J"T-9"{RB}, [T]9, [9]8, [8]7, [A"T-9"], [KT], [QT], [J"T-9"], [T"9-8"], [9"8-7"], [87], Ah8h, Ah7h, Ah6h, Ah5h, Ah4h, Ah3h, Ah2h, KhJh, QhJh
2 55.8 53.0 5.7 [Q]J