To piggyback off of @Cutlass, the Saturday Night Rule is designed to take advantage of business travelers' demand inelasticity. Business travelers generally don't have as much leeway as leisure travelers to stay over for too long. They are, at least theoretically, on the clock, and the company often doesn't like its time being spent somewhere else where it is more difficult to work even if the price in travel reimbursement is lower. And a company isn't going to cancel a business meeting over the price of a plane ticket.
So airlines can get companies to pay more to send their people home at the end of the work week.
Low-cost airlines attempted to circumvent this concept for awhile last decade, but it petered out pretty quickly. Businesses prefer relationships with specific airlines, limiting the extent to which low-cost carriers can supplant them. The discriminatory pricing really hits smaller businesses and leisure travelers without the give in their schedule to accommodate an extra night's stay, but their demand is inelastic too so they just get screwed.
