The Holland international was out of action for seven weeks with a toe injury.
He made his return late in the FA Cup tie at Liverpool last Saturday when he went on as a substitute in central midfield.
Wieffer has generally been used in a version of the right-back role since the late stages of last season.
He was originally signed as a deep-lying central midfielder and looked set to play that role for the newly-arrived head coach Fabian Hurzeler as the 2024-25 season got under way.
However, his campaign was badly affected by injury.
Solly March training hard (Image: BHAFC/.Paul Hazlewood)
He adapted to the right-back role in the later stages of last season, really winning over fans during the 2-0 win at Wolves.
Albion have not found a dominant deep-lying midfield man this season although Carlos Baleba and Jack Hinshelwood have both had their moments in that role.
James Milner did a decent job in the heart of midfield at Aston Villa last week.
Also of note from a set of photos by club photographer Paul Hazlewood during Wednesday’s training session were shots of Solly March hard at work.
March made his first return from a serious knee injury in the home fixture against Brentford last season.
But, after four months of regular action, he has not featured since last April.
Hurzeler said last week the popular winger had played a full part in a lively training match with the under-21s.
There has been no indication as to when March will return to action but, should Hurzeler and staff see fit to re-introduce him via the 21s, there is a PL2 game at home to Birmingham on Sunday.
The group training included young goalkeeper Lorenz Ferdinand, who is on loan at non-league Havant and Waterlooville.