Weatherford was a key contributor in the team's run to the Super Bowl championship, both as a punter and a holder on kicks.
"What a blessing to have another opportunity to be a NY Giant for at least another season. God is good!!!" Weatherford tweeted.
Weatherford will be paid roughly $2.5 million, the average of the top five salaries at the position. If he signs with another team, New York will get two first-round draft picks.
It's the third time the Giants have used the franchise tag. Running back Brandon Jacobs got it in 2009 and Jumbo Elliott in 1993. Jacobs signed a new contract less than two weeks after being franchised.