Hi,
These are always fun spots because they can become a bit of a leveling war. fwiw, I think your line is a decent standard option.
Even though our hand is a bit face up for our opponent (weak SD value, probably A-high) he doesn't know if we're calling or folding.
When we check our opponent is getting 6.3:1 on a bluff attempt. For us to remain unexploitable we shouldn't fold over 14% of the time because otherwise he profits immediately from betting with any two cards.
If we look at our hand range when we 3-bet pre, bet flop & turn, check river... decide how many hands we have, how many we should fold, and then usually fold the worst ones.
Calling here is probably a good default play until you know something about his flop/turn calling and river betting tendencies.