So the 8 on the turn isn't the ideal card although it affects both of our ranges the same. As for my actual hand though, not only does it imrprove some of his 8x which he might have a maximum of 6 combos of (87s,89s,A8s) but it also reduces the amount of hands JJ gets value from on 2 more streets.

I'm not entirely sure what's "standard" here. My range is going to consist of a bunch of flush draws, overpairs, trips, give-ups, and the occasional boat/quads. His range should contain the occasional boat/trips, 99-TT, 77, 76s/A6s, a handful of draws, and floats.

So what's best? By check/calling his floats might bluff us off our hand if the river is nasty while putting our hand face-up to basically what we have since we wouldn't have any draws. Betting seems ok since we'de like to do that with our draws but I feel like his calling range narrows significantly when we do. In the actual hand I decided to checkraise since we pick up more money from his floats/bluff-catcher type hands that might bet turn for a showdown but I'm not sure if it's better than betting...