OK im glad you checked now with us checking our target will lead out and what we have to think is from the way he sees how we played the hand out.
1. We used the button to raise pre-flop ( and we could be doing this with small suited connectors and  a large range of hands ).
2. He knows we c bet out 80% of time and again we do and he calls so no shock there.
3. Turn check check, now with him seeing this he knows  he can make a stab at the river which he does, i hate that the ace got there but it did.
Now as we said earlier what does our target limp in with and call raise OP.
1. Small pairs 22-99 looking to set mine?
2. Suited Aces?
3. Suited broadway cards? Suited Connectors?
4. Weaker Aces, ACE 8 - Jack
5. Mid unsuited connectors 7-8 8-9 9-10 10-J 10-Q.
We could go on if a complete fish it could be any 2.

So if we look at flop from his point and say we have hit the flop with maybe Jack 10, even though we have top pair if we bet out and get reraised we would be in a tough spot so his check is natural as he knows we are c betting the flop, now if we reraise and get raised back we have to give up as its to tough facing bets OP, so check call is what he does, turn brings the scare card and both check.
Now seeing this check and knowing we could have any 2 from the button i would bet the river to put us to a decision which it has.

Now our target bets full pot, what does that tell us? Well he saw us give up the betting on turn so his hand could be complete air, betting full pot looks like he is trying to take the pot away from us.
In this situation he could have Ace clubs and # and knows we dont have nut flush so bets out, would he call a bet with bottom pair and an ace? 
  Your option of raising is a good point as you say his bet doesnt look like a value bet that wants a call, i would need more info on his stats to know what his folds to reraise are on river as you could get him to fold a better hand. 
Ok so im not folding and not having info on reraise i would call, our 2 pair could still be good, it prob isnt as you wouldnt have posted this up and he shows Ac 5d.  But the info that we gain will pay for us over hands played with this target over time.

Ok so no more action here so its time for the big reveal, lol

As Slim said I was expecting them to lead out, but probably because I am pretty new to cash I don't see a pot bet as a value bet, so I read this as an overbet to take the pot, I also was pretty sure this was not a spot to re-raise as they would either fold or come back over the top, prob shove (I know I would if I had it). so now i'm thinking they missed all there outs and have taken my week flop bet and turn check as a sign that i was not playing with much so am now thinking bottom pair maybe, missed flush or straight so have no choice but to call I feel.

now before the picture, what they did have did surpise me a little, but was in the range I had them on near the start but not what I expected after their river bet.

 

I think given their actual hand I could have raised the river and got more chips, guess I'll never know....but that is the difference being in possesion of all the facts makes.

The reason I posted this particular hand is I thought this river call was dangerous and reckless and that I was lucky it paid off, with so many hands that could have just got there I think I should have folded and from the 2 opinions of the river posted above it looks like it was a 50/50 to what I should have done.

I hope this get some more posts now all the information is out, and I hope people follow it through rather than just posting based on all the facts

If you raise the river you wouldnt have got another cent think you played it just how i would have , you set it up right and even if club had fell we would still make the call its such a good card to rep, and like grump says you can make these plays on certain targets as grump points out he doesnt like the call on the above board but with the stats and hands you have played with him you know he was making a stab, like you say hes betting 60% of rivers in that postion is very spewy, you now have more info and a good target to follow.
If we look at it from his play he makes  an error on turn unless he was hoping we would bet, but from turn he could have won this pot even though we hit giving us 2 pair, with a bet into us its played out differntly.
I have 1000s of hands in simalar situations and its a very high % that once they have money invested in the pot and by playing hand as we have above they will make a stab at the pot.
Glad you won it.