
You didn't list how much were in your stacks, which gives no indication of how much of an overbet "this guy" made when he went all in.
You said this guy goes to showdown, but you didn't indicate if he was the aggressor in these cases. It's one thing to call down with middle pair but not many people are going to go all in with it in a small stakes tournament on the river when the blinds are still so small. He made a good bet, hoping you would make a "hero call", which you did.
It's not a crime to fold the best hand in situations like these. 90%+ of the time when people make this kind of bet into you when they are first to act in small stakes tournaments have the nuts, or close to it (to this guy any straight was the nuts). When it only takes a K to beat you (which you very well may have had in your hand) then there is no reason to call if you still have a lot of chips left when it is so early in a tournament like this.
You correctly kept the pot small on the turn by checking, then made a huge mistake calling on the river.
What you said on the flop was the key "He contemplates it and almost folds". He would not have thought that long with a jack, certainly not with an ace. He had to be chasing something. If he has 10,000 in his stack he's going not going to look at pot odds, he is going to look at how much it is to call compared to what is in his stack.
Personally, "hero calls" are the way I make most of my chips in tournaments like this, because no one ever believes the overbet could really be from a strong hand.