The new deals run through to 30 June 2017.
Eighteen-year-old Weaver has been with the Club since the age of 12.
A boyhood Blues fan, he is a former pupil of Tudor Grange School in Solihull.
He has gone on to play his way through the Club's age ranks to figure for the Under-21s. He has made 11 appearances for Richard Beale's Development Squad side so far this season
Cogley, who is two years older than Weaver at 20, has been at St. Andrew's for five years.
He has predominantly figured as a right full-back, but has also slotted in on the left when required.
He possesses plenty of speed and stamina and likes to get forward. Cogley has 14 Under-21 appearances to his name during this year’s campaign.
Meanwhile the Club can confirm that midfielder Liam Truslove and defender Perry Cotton will be released when their existing contracts expire on 30 June 2016.
The Club wishes both Liam and Perry every success with their future careers and thank them for their contributions over many years.
Truslove has been with Blues since the age of ten, with Cotton here for a similar period of time.