The info you have A.A. Weathers is also all I've found.

Henry and also a Chris Weathers are listed in Company B, 44th. Regiment.
Company B was known as the Mississippi Swampers and was raised in Coahoma County.

Here is a history of the 44th., there is link to the Ms. Dept of Archives at the bottom of the page should you desire service records.
http://www.mississippiscv.org/MS_Units/44th_MS_INF.htm

Henry Weathers (First_Last)
Regiment Name 44 Mississippi Infantry
Side Confederate
Company B
Soldier's Rank_In Private
Soldier's Rank_Out Private
Alternate Name
Notes
Film Number M232 roll 43

Chris Weathers (First_Last)
Regiment Name 44 Mississippi Infantry
Side Confederate
Company B
Soldier's Rank_In Private
Soldier's Rank_Out Private
Alternate Name
Notes
Film Number M232 roll 43