The athletic commissions require fighters to weigh in the day before an event. If the fight is at Welterweight then both fighters need to come in at 170 pounds. You'll often see fighters come in 1 pound overweight which is perfectly legal. The athletic commissions allow for fighters to be 1 pound over to make up for any scales being off.
If a fighter comes in overweight they are given 1 hour to make the weight, if they are not able to then the fighter is penalized half of their "showing" pay (Someone correct me if I'm wrong)
In smaller shows opponents can accept a fighter at the weight they are, or if they are unable to make the weight after cutting, refuse the fight. This happened to Demacio Page on the Tapout show. He came in 1 or 2 pounds over and his opponent forced Page to cut the weight or he was going to refuse the fight. These situations usually don't happen in the UFC since fighters are there to fight, too much money was invested in the training camp to call the fight off at the last minute.
If the fight were scheduled to be a title bout and a fighter didn't make weight, the fight would no longer be a championship bout. Like Cheal Sonnen vs Paulo Filho II
I hope that answers your question.