I would def. bet atleast 10 into that pot and not try and Check call. Your giving him advantage there. You can possible protect from him raising 35 by betting in 10. If he has the 6 (his starting hand is either A6 or 66)....either way your behind. But if he has the nuts he would most likely call and then break it hard on the turn with the blank.

At which point you might want to reconsider your hand.
It is possible that he is trying to protect face card pocket pairs....but unsure....