Common spot.

We 3bet in SB with QQ, 1 call, flop Axxcch high. We make the "standard" x/call. Turn x check again. Now my question is, if we perceive villain as competent aggressive, how should we combat our rather obvious range caption when villain adjusts by auto doublebarreling? Should we x/call turn wider, should we strenghten our flop checkign range with hands that want to go 3streets for value, or do we just give up anytime OTT? Is it favorable to have a uncapped c-betting strategy as we expect villain not having a wide enough raising range to always b/fold flop with QQ?