Playing back at him for that reason doesn't really make sense. I really doubt 10NLers double barrel without some sort of draw/hand so I don't see how he has A high here ever. He can easily have A7/T7s/97s/76 here as well on the river so keep that in mind. You are right that diamonds rarely c/r the river but semi-possible. The main thing here though is that he is so rarely double barreling with air that I just fold turn (on the turn you can throw in overpairs/86/75/55/33 as well).

If the river was a 4 no I would not bet. I do not think you are getting called by worse here at all and are often still behind even when you check.