Price discrimination (in the neutral, economics sense of the word). Business travellers, who are usually willing to spend more, were/are viewed as being less likely to stay a Saturday night at their destination. Putting in a Saturday night stay requirement allows the airline to charge more to business travellers without losing leisure travellers who are more price-sensitive.

Of course, there are business travellers who stay a Saturday night (either because they're savvy about airfare or by coincidence) and leisure travellers who fly without spending a Saturday night. But that's the general idea.