The 6-foot-5, 305-pound Weaver is a New Orleans native who last season entered the NFL as an undrafted rookie out of Southern Mississippi.
Weaver first signed with Tampa Bay, but was waived during the offseason. He then spent training camp with Cincinnati before moving to Miami's practice squad during the regular season.
The addition of Weaver gives the Saints nine offensive tackles, six of whom have a season or less of experience.
Givens joined the Saints in 2012 as an undrafted free agent out of Miami, Ohio. However, he spent the past two seasons on injured reserve.
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