These installments likely don't cost Klarna any extra. You can play games with the credit card authorization system to simulate installments without incurring extra fees. Then Klarna has their own middleman fee like any other payment gateway, and it's very high despite the lack of extra cost.
4 instalments spaced by 2 weeks with the first up-front averages out to about a 3-week float, which is less than the grace period on ordinary consumer credit cards in the US. And Klarna charges merchants more for this!