My wife and I will need to store one (maybe two) pieces of luggage for 10-14 days in Glasgow; hopefully at or near the Central Train Station. We will arrive at the Central Station, then soon depart for Edinburgh. I read that the main bus station at Killermont Street is a secure place for luggage storage but this would require going from Central Station to Killermont Street and back to Central Train Station. Each of our pieces of luggage is approximately 16" x 25" x 10" (40cm x64cm x 26cm) and each weighs about 25 pounds (55kg).
If you visit this page http://www.nationalrail.co.uk/stations/GLC/details.html
and scroll down to Staffing and General Facilities you’ll see details for left luggage at the station.
There are several places to store in Edinburgh too.