Steve Weatherford does some extra things as a punter the team should consider where evaluating him.
He has been the holder on field goals for a chunk of his time with the Jets. He has generally shown soft, reliable hands and rescued a few bad snaps. He has also shown that he cannot throw the ball well to escape a broken play as a 2009 overtime try aborted due to a bad snap showed. The Jets gave the job to Kellen Clemens because of that play during that year, but it is a rare happening.
Weatherford has also shown himself to be a very good athlete executing fake punts. The 6'3" 215 pounder looks very comfortable carrying the football. He did the heptathlon for the University of Illinois track and field in college.
While he has not had to placekick with the Jets, he has experience doing so. He kicked off in college during his senior year. He averaged just over 60 yards per kick. That is not great. It is actually worse than what Nick Folk did in 2010 with the Jets. Why is this important? Kickers sometimes get hurt. Think about Detroit losing its kicker against the Jets and having Ndamukong Suh kick. Ideally a punter would be able to be a successful backup kicker. Weatherford might not be that, but he at least has shown he can do it. Some might scoff, but I remember what a fiasco it was when Ben Graham tried a kickoff for an injured Mike Nugent in a 2008 game against the Dolphins.
Finally, Weatherford is tough. He had an irregular heartbeat act up in the 2009 Playoffs against the Bengals and literally needed the coaches to drag him off the field. It is nice to have a competitor for a punter.