BGC will be conducted by whichever CPC or VO your application was forwarded to - I assume CPC-Mississauga. They will look into the authenticity of his Police Certificate and other security measures that will prove he's not a threat to Canada. They will also look into the other forms that were submitted and signed by him to check for inaccuracy and truthfulness.
Spousal sponsorship is mainly divided into two parts. Checking for the sponsor's eligibility and checking for the PA's eligibility. If your application is already undergoing BGC, then the sponsor must have already been deemed eligible. They're now checking for the PA's side.