Final answer:
Airlines use Saturday night stays to differentiate between business and leisure travelers, charging higher fares for business travelers who prefer not to stay over the weekend and lower fares for price-sensitive leisure travelers willing to stay.
Step-by-step explanation:
Airlines care whether you stay over a Saturday night because it helps them segment the market between business travelers, who are often less price-sensitive and may not want to stay over the weekend, and leisure travelers, who are looking for more economical options and are more flexible with their travel dates. By offering lower fares to those who stay over a Saturday night, airlines can attract price-sensitive leisure travelers while charging business travelers, who typically prefer to return before the weekend, higher fares due to their willingness to pay more for convenience.