I am by no means a heads-up specialist, but here is my take on the hand:
Preflop
Checking seem very standard here. No reason to go crazy out of position with suited junk like this.
Flop
You connected, so folding is clearly not an option heads up. You could however go for a check-raise to protect your hand, since your pair is so small. It sucks, if you get action, but when you check-call, all turns are going to suck as well, unless you improve, or he check back. I could go both ways here, so just mentioning, that there was a different way to play the hand.
Turn
As played I would probably just fold now, unless you had a feeling, he had been completely out of line. You have a very bad pair and no draw, and his bet was pretty large.
River
First of all I dont agree, you are always behind. And if you think so, why did you call the turn bet? You can not call such a large bet only hoping to hit trips or two pair. You still beat busted clubs and air other than the air, that rivered top pair. So I think, you have enough showdown value to check and basically hope, he gives up and check behind. You dont however have enough showdown value to check-call. But this is the time, you can consider turning your hand into a bluff by check-jamming to really represent a 4, especially if his river bet is on the small side.
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