Try not to post with results in the future as it might affect the advice you're given.

The turn check is fine. It's very unlikely you're behind by the river. The only Qx villain should have is AQ and I'd expect that to bet turn since it basically hit its nut card.

Other hands that could be in villain's range: 66-88, TT, JJ, T9s, 98s, A2s-A5s, A9s, 87s, 76s and some AK, AJ type hands. I omitted nutted hands because I think it's unlikely villain will check back something like 99 and even when they do it'll likely be a mixed strategy where he bets most of the time and checks sometimes.

Against such a range you only really gain value by checking from 87s 76s as I think most gutshots like A4s will just check back river. There is a lot to be gained by betting though. His range, if he's not slowplaying, should be fairly weak and if likely 9x at best. Against that type of a range I like a small bet of maybe $4-5 on the river.