According to Pro Football Talk, the Giants inked Weatherford to a five-year, $12.75 million deal. He'll be staying in New York for the long haul.
Weatherford was an undrafted free agent (as most punters are) with the New Orleans Saints prior to the 2006 season. He played two and a half seasons in New Orleans before spending time with the Kansas City Chiefs and Jacksonville Jaguars. He played in New York, but with the Jets, in the 2009 and 2010 seasons before joining the Giants.
The Giants have been relatively quiet in free agency, adding TE Martellus Bennett. But I guess when you're the defending Super Bowl champs you don't need to be too aggressive in free agency.