I suppose you could bet really small on the turn, but it's such a rare runout that I'm not gonna give it much thought. (I don't show up with trips or QTs in this spot, so I'm not sure how to balance a betting range). There's clearly no harm in checking back, as it gives villain a chance to bink a flush/straight, or make a river bluff.
I thought small bet over checking the turn too. As silly as it sounds an overbet shove could get looked up *extremely* light on the turn, far lighter than your river shove will usually get looked up.