The Giants and Jets are always going to be attractive alternatives for free agents the other team has. Since they play in the same place, a player who signs with the other will not have to uproot himself or his family.
On another note, I hope the Jets find a way to keep Weatherford. I know they seem to like T.J. Conley, and keeping Conley could save a bit of money to sign another free agent. Despite Steve's bad postseason, though, he had an excellent 2010, pinning opponents inside the 20 better than anybody and kicking a generally difficult to return ball. It might have been a fluke year, but considering Gang Green's chronic problems finding a quality punter, I think it would be worth giving him another year to see whether he really has turned a corner.