Let's take a look at today's hand:

Let's assume that you're sitting in Seat 2, up there in the top-right corner, and you're dealt a good starting hand, Ad Qs. You're on the big blind. The player in Seat 4 makes a nominal raise to $1.50, and the player in Seat 7 calls. Every other player folds to you. Given your starting hand, you call the extra dollar.



How Would You Hold 'Em?
Well, I'm not going to hold them at all. While this player might be trying to buy the pot, I just don't see this player making this bet unless he's got a king. He checked the turn because his kicker was weak and he interpreted your call on the flop as a sign of strength. Then, when you checked the river, he assumed that you either missed a draw or didn't hold the king, and will come out betting for maximum value.
I might have thought that he was bluffing if the bet was smaller, say another $2.00 bet. But the size of the bet on the river (relative to the size of the pot) gives away his king, as he's trying to get a sizable chunk from you and he's putting you on a hand weaker than his.
Here's a video of how the hand plays out. If you'd like to expand it to full-screen size, simply click the icon in the lower right hand corner.