I guess the first point is obvious, if we are 53% vs his range we should NOT 3-bet pre-flop. We will only fold junk we are beating and don't have that much equity anyway.

I think I might check/fold terrible flops like AXX (paired+X) or ATX all suited to something other than you.

I think check/calling on a totally blank flop is bad, leading or check/raising much better.