here's an excellent
thread over in SSSH that deals with this concept brilliantly.
the underlying concept here is that inflating the pot even when you have neutral equity is -EV when you have to peel again on a whiff.
It doesn't apply directly to this turn play, but abstractly I think the thought process has merit.
In this example though, betting the turn is only correct to the extent that
--button would not have raised
or checked through the turn
and
--button would have called a bet on the river if you had bet the turn, but would not have you had check/called it.