I'm still not sure about this but I am more and more leaning towards checking behind, mainly for the reason that it's tough to see him check/call the turn with worse except KQ maybe. The
other thread on SSNL advocate that villain should fold TT on this turn, Spurious said he liked a check/shove. I think majority of people (in villains shoes, not heros) is not going to check/call that turn with many worse hands. Hands like A
Kx, could go for a c/shove as well or are probably double barreling. Not very often that people check/call a drawy board on turn in a 3bet pot with A high.
Therefore I really don't like bet/folding AQ here if I'm expecting villain to fold or shove.