https://gg.gl/gn8h0

Need some help on how to play turns after checking flop IP as a PFR and the OP players checks again to me on the turn.
In this hand the flop is bad for me so I would use a polar betting range with a bigger size, QJo would go in my checking range. The turn is a Q, I think it's a better card for my range than his, I can have more strong Q combos like AQ, QK, QJ that he can't have since he would 3bet them preflop, After he checks for the second time it's unlikely that he has flushes, straight or sets. His range looks pretty weak so I think I can bet with a high frequency here. I'm not sure what size to use, betting big doesn't really make sense to me, strongest part of his range are weak Q pairs like QTs, Q9s, maybe 99, 98, T8 and I think he would fold those hands to a large bet, so betting something like half pot and extracting more value from those hands seems like a better choice.