You get dealt 7♣-6♣ in the BB. UTG limps, the CO (who posted a late blind) checks, the SB completes and you check. You flop trips: 7♦-9♣-7♠
The SB checks, you check and UTG bets $3 into the $4 pot. The CO and SB fold, you call. Pot is now $10.
The turn adds a diamond draw: 3♦. You lead for $5 and UTG calls. Pot is now $20.
Diamonds get there on the river: K♦.
What do you do?
Reads: an unknown player limped UTG. Sometimes people get tricky with QQ+ and try to limp-reraise from EP, but you see less and less of that these days; the players are getting too good as a whole for that transparent play. On the other hand, you do still see weaker players limping in with small or medium pairs from upfront, hoping to catch a cheap flop and set mine. You might also see someone do this with big (but not huge) suited aces; maybe ATs-AQs, and possibly KQs.
The board is fairly dry. The action gets checked to the UTG player by the blinds, and he's only got one person to act after him (the CO). The CO has demonstrated fishy propensity (i.e., by posting a late blind). The paired board probably didn't hit the CO, so the UTG player could simple be trying to take down the pot here with most of his range.
When you call and then lead the turn, the UTG player has to assume you have some kind of hand. When he just calls behind to your donk, it feels like he's trying to pot control and see a cheap showdown. He could also have picked up a backdoor flush draw, but this is a small part of his range. I still think he's got a small or medium pair here.
The river King does not change much other than letting the backdoor flush get there.
Estimate: You're pretty far ahead of most of his range with a lot of hand equity.
Decide: You've got a solid value that is either way ahead or way behind.
Implement: If you check, with the intention of raising, he may not bite; we said earlier that he could easily be trying to see a cheap showdown. I prefer to bet out here. He'll call you with a lot worse, and if he raises, you can safely let go of your hand. I'd fire out for about 2/3's the pot.
Answer: Bet/fold river.
All-in for now...