Full agreement on preflop and flop, standard. The turn is hairy but probably a bet / call. If we're not betting KK here I suppose that means we are checking with all one pair hands? Would we bet AA? We do block the KT nuts and unblock tens which is a positive. We can certainly be called by worse hands, so perhaps we can be a bit more aggressive, but I certainly understand the check. River seems good as well, just check call, pray.
I think it is close but my instinct is to bet the turn. Given how big the pot is, you are going to get called down by too many hands, and when you're behind you're basically never drawing dead here. Plus, people will call with worse here substantially more often than they will bet themselves with worse.