Firstly I would have folded this hand and not even been in the pot. However given we are I reckon he has AQ/KQ as this would be consistent with the 4x raise, or perhaps even an overpair like 9s or 10s. Also, you mention about calling to try and hit the straight. This is bad play because you are getting bad pot odds. If my maths is right on the turn river you are getting odds of 2.6:1 and 2.18:1 when the chances of hitting a 7 are more like 10:1. And the 6s could feasibly give him a flush. Even using implied pot odds calling those bets for the straight cannot be justified. I will be interested to see the result