In the good old days, as I understand it, a saturday night stay fare was classed as a leisure fare and therefor discounted. A non saturdaynight stay was more of a business travel ticket so BA could squeeze more revenue from them pax.

A lot has changed and you dont see the sat night rule applicable on short haul fares ex-uk. It is still however prominent on long haul fares. I suppose its in line with other carriers so certainly nothing unique at BA.