Welcome to Flyer Talk lizzyteacher

I assume this is all on a single ticket.

When you check in at STL with United they will check your bags through to GLA. Thus United baggage allowance applies.

On the return when you check in at GLA they will check your bags through to STL. Thus bmi baggage allowance applies.

The baggage allowance for this should be 2 pieces per person (or 3 if flying business class), but each airline may have it's own maximum weight per bag limit. As far as I know, bmi's maximum weight per piece is 32kg but United's is 23kg for non-Star gold status passengers flying economy (or 32kg otherwise).

If you have separate tickets please advise which flights are on which tickets because this affects the answer.