i like checking behind here. seems to be a way ahead/behind spot and at these stakes i doubt he's folding anything that beats us, plus we have the gutshot + two overs as outs against most of his range. if we bet he either

a)calls/jams with the part of his range that has us dominated (all pairs)
b)folds the part of his range which is drawing dead to three outs (aq,ak,aj,kq)


i doubt he check shoves air here, but if he does, thats a tough call with AK high getting roughly 2:1

also, history indicates he may raise a wider than normal range preflop, but does he really call 3.5x 3bets OOP with 66+,AJs+,KQs,AQo+,KQo?