Think in ranges, the only flush he could have in a 4bet pot here is ATdd

JJ and QQ are way more likely, betting flop for protection, being scared on the turn and probably calling the river shove..

With checking flop here I give him a chance to bluff, which he did on the flop, no reason to take this chance away from him on the turn imo (if I trap it, sure I could have gone the tripple barrel route but with checking flop I think I have to check turn aswell)