There are a couple of hands beating you that might fold to a c-bet, but I don't hate checking here either.
Once he checks behind I would lead the turn for sure since you said he's fairly straightforward. You can probably get away with leading the turn with less, something like 400, and not look as weak as if you bet that amount on the flop.
As played I would fold on the river mostly because of stack sizes, plus I don't think you're ahead often enough to call especially once you take in $EV considerations. This might actually be a decent spot as played to make a blocking bet on the river. Maybe not necessary against a straightforward player but since you said he's been turning up the aggression a bit a defensive bet here might work nicely. If he raises it's an easy fold and cheaper than your crying call.
Edit:
I'm not a huge fan of blocking bets. Here is my normal thinking OOP on the river:
<ul type="square">[*]If I'm pretty sure I have the best hand I bet even if it's a thin value bet (especially early on) [*]If I'm not certain I have the best hand, say it's about 50/50, then I'll check/call since you're usually getting at least 2:1 to call. You don't hate if it gets checked down and you're going to pick off additional value from bluffs.[*]If I "might" have the best hand but I can't call a bet of 2/3 the pot or larger then I might lead for 1/3 the pot. The more straightforward and passive villain is the less likely it is I'll actually try blocking.[/list]