Weddle signed a five-year deal worth $40 million back in 2011.
The Falcons recently locked up S William Moore to a five-year contract worth $30 million that included $14 million guaranteed.
Byrd, 26, is two years younger and doesn’t have the same injury concerns as Moore, which should translate into more money for Byrd.
As of now, Byrd will make a guaranteed $6.9 million salary for the upcoming season after the Bills franchised him last week. Buffalo will have until July 15 to negotiate a long-term deal, but Brown notes that contract talks “are not on the front burner right now.”