put/throw your weight behind something
put (one's) weight behind
To wield one's influence or power to support or promote something. The small-town candidate is hoping the state senator puts his weight behind her in the race. If we can get a corporation to put its weight behind our charity campaign, we can raise even more money.
throw your weight behind something
COMMON If you throw your weight behind a person or plan, you do everything you can to support them. The U.S. government is promising now to throw its weight behind the peace negotiations. Northern Ireland's three newly elected MEPs have all thrown their weight behind the campaign. Western governments have thrown their weight behind the leader.