Echo comments about way the hand was played,
but I'm interested in the reason for you calling the river. Psychologically, people like celebrating success. It is a common thing to hear someone you know in any context say that something has gone well and want to share their joy with you. Not a brag, but a genuine and honest expression of joy. Poker sees a lot of that. How many times do you see people show aces when everyone folds to their pre-flop action? Why is that? We instinctively want to share our achievements and, as daft as it sounds, being dealt the best possible starting hand is an achievement.
Any desire to show cards may be taken as a desire to share an achievement. "I'll show you if you fold" is frequently a way of saying "Hurry up and don't throw your money away; I'm bursting to show you and everyone just how good these cards are!"
There are exceptions, as with every good rule. Some people will only show bluffs and this can be a way of demonstrating power and dominance over the table.
It is a way of showing who is in control; who is boss. Where a player is identified as a threat, this is more common, as the alpha male will seek out the beta male to humiliate them and put them back in their place in the pack. In that case, a desire to show the cards can be a desire to show a winning bluff. To test the theory, if you think Villain shared your view that you were the only two good players at the table and if you think it is likely he would be inclined to pull that sort of move, you can test him with a question that challenges his dominance or you can take a view on it and decide how important your image is (remembering that a weaker image than you play is normt a bad thing).
If he asked you the question just as you were going to fold, it's likely he was saying something to change your behaviour and that would mean he wanted you to call, which signals extreme strength. I'm expecting that isn't what happened here.
You might think all of this is irrelevant mumbo jumbo. It's one of the main reasons I love the game

I don't play much live poker. Hardly ever. I used to think it would be a lot easier to get "tells" live than online. Because i've played so much online now, though, it's so easy to get tells, mostly bet sizing tied up with how the player has been playing in general.
I don't really agree with the whole psychological aspect. Especially the 2nd part in bold. It's a table of limpers, some1 will limp and call a raise. Others, like the guy on my right, would limp and always fold to a raise. The 1s who limp call are always folding when they miss. At this table if the villian in this hand, he seems okish, but i'm going for value against the other players.
Maybe it is his attempt to try and assert some authority over the table, i would just imagine he's trying to get me off the hand. Don't think there's anything much deeper going on here. Sure if i fold he maybe flips over his cards to show a bluff. Would this mean he is the big man? Not really imo, he's bluffed 1 hand. I would just think nice bluff, onto the next hand. Naturally in poker there is a psychological aspect, a big aspect, but i would say the whole alpha beta thing is just over complicating things, and would say that's not really at play.
Why i called the river.
I never mentioned this before what happened was, after i bet the turn he went to raise. He put in an amount that was 2 small. So he had to make up the difference, so in the end it was a min raise. I suppose it was a bit odd that he had fumbled with his chips, and got the raise size wrong. I felt it was a bluff here and am pretty sure he just checks the river.
For some reason i had it pegged he would raise a set on the flop, given how deep we were. I know it's a dry board, but felt he wouldn't slow play a set on the flop.
The river another K, i'm loving this card when it drops. Pretty sure he doesn't have a k. As per the turn, i'm sure he's checking the river.
When he fires quite a chunky bet on the river i'm hating it. Normally i make quick decisions, online i have 15 seconds to make a decision!
I kept saying outloud is it a set, and chatting away, he wasn't budging there was no reaction. All the time i'm talking through the hand (out loud) he's giving nothing away. I was closeish to folding. I was thinking he's saying he has a set by his bet size (FH now on river). I don't think i ever considered it was a king tho it could have been. It was only a flopped set that was worrying me.
I was thinking, and this guy not involved in the hand chirped in that he was calling time. I don't even know if people not involved in the hand can do this, and without a tournie director being there. I didn't pay to much attention to this guy he has just limped pocket jacks 2 hands previous!
Before the guy had shouted time i had counted out the call. To see how much i had left behind, if i call i'm still above average stack wise (i doubled up the 4th hand).
The opponent said something 2 me, and for some reason i just announced call and snapped my hand over.