I have to disagree there Carroters. For me OP's line is quite likely AK/AQ for the following reasons:

* Standard sized c-bet when first to act
* 1/2 pot-sized second barrel on the turn, typically for pot-control or a scared second barrel not wanting to risk a lot with a weak unmade hand
* Checking the river after barreling previous streets + pfr when no A/K/Q hit on the river and the flush missed in case OP had AK/AQs

I do agree that it would be a terrible board for a second barrel IF the second heart hadn't hit....now an AK/AQhh hand can be double-barreling with extra outs to the nf and again this is what makes the river check look so weak. Any hand with an over-pair to the board would have still barrelled the river with aabout $1.80-$2.50 valuebet. Do this and then we can talk about finding reasons to not fold to the shove.