What else am I doing with these aces??

[HajiShirazu]

You need to bet here to charge all the hands that will get half the pot off of you if another heart falls on the river, and/or possibly get called down by worse hands. If you get checkraised call and fold the river.
The exception is if you knew this guy was big on bluffing and you would have to call his c/r+ riv lead or river donkbet. Then you could consider a check.