The phrase "roots for" has a few different synonyms that could be used in various contexts. One option might be "cheering for," which is a more common expression that conveys a similar sentiment of support and encouragement. Another possibility could be "backing," which implies a stronger level of support or advocacy. "Encouraging" or "motivating" could also be used to describe the act of "rooting for" someone or something. In some cases, "promoting," "fostering," or "advancing" might be appropriate alternatives, particularly if the focus is on helping to develop or grow a particular individual or cause.