I would say that "support" is a little bit stronger of a word that "in favor of." It gives the impression that a person is actually doing something to help out. Do you mean "sustain"? That means that someone is doing what is necessarily to keep something going. For example, food sustains a person physically. Without the food, a person would die. So, "sustain" is stronger than "support." I have never heard the phrase "plunk for," but is seems like it would be similar to being in favor of something.