Here's my opinion –

As I was reading it, I heard “bet the turn” in my head.

I think I understand why checking is/could be good – keeping complete air hands in, keeping the pot small with a good hand so as to lose less vs hands that beat us, and maybe more reasons like underepping and setting up a river bluff by villain?

But in this case, I think first of all most air hands have lots of outs to beat us, or make it easier to bluff us with the best hand.  Of course you can decide to call his river bet if that's the best move, and maybe you would have – if so I am likely to be often making the mistake of folding too often to a river bluff by villain. 

Whereas if we bet we can get value from pairs below T, and make high cards, draws and broadways decide if they want to fold, continue with the worst hand or try to bluff us off the best hand.

I suppose this idea may be too susceptible to being check/raise bluffed?

If we bet turn and he calls, I think I would call many river bets even on some scary rivers, and suspect that I should be calling even more, and check most rivers if he checks first.

I agree that we're trying to get money in on the flop because turn and river cards won't be good for us.  But I wasn't in the mind set of trying to get it all in. I don't know though.

I figure yeah they are Cbetting a lot, but they do have plenty of JQ, JK, JA and overpairs.  If we try to get it all in on the flop they will obvious not do it with worse, but if we try to do it over several streets I feel the bad turns and rivers for us (good ones for the opener) come into play.

Good questions, but I certainly don't know.