Over betting is an advanced tactic that a player can use to get action on a hand when no other action is likely. There are two situations where the bet will work well. The first is against a novice player who doesn’t really have a concept of the value of the chips in front of him. You can over bet a nut hand because they’re likely to call down anything as long as you don’t say “all-in”. It won’t work every time, but when it does you get lots of value on your hand.
The other time that this play can pay you off is against a good player who will recognize the over bet as a bluff attempt. They put you on the bluff and make a hero call with a smaller pocket pair or second pair. Against a good player a regular value bet would be recognized for what it is, and you most likely won’t get the action you’re hoping for. If you can construct a betting pattern that that player will interpret as a bluff, you may get paid off. It will help if you’ve been playing aggressively at the table prior to the move, which would make the over bet look even more suspicious.
The only time it really makes any sense to make an over bet is on the river. It can work before or after the action is checked to you, and it should be at least one and a half times the size of the pot, or more.