I would still bet turn too. A passive limper will call with all kinds of stuff we're ahead of and can get value from like Kx, weaker 2 pair, Ad4x, 78, etc. Probably just bet it for 40. We can easily fold to a check raise.
I'm fine with either bet/bet/betting (evaluating if raised) or check/tarping. If checking to tarp, I would likely just check/call flop/turn and perhaps even river (opponent dependent, the more blasty the more I just check/call the whole way, the more ABC the more I might donk the river to prevent a check/back).
As played / runout, fine with turn and now I do a small river bet/fold of like $30.