A simple answer this is not.  Your question, basically, begs for an explanation of economics, specifically as applied to the airline industry, but to any business enterprise.

The whole idea is to have more money coming in (income) than going out (expenses) over the useful life of the asset (airplane).  No, one flight won't pay for the airplane, but if the airplane is to serve a useful life of, say, 10 years with the airline, it better bring in more money, over those ten years, than it costs to fly it (including maintenance), and to cover additional costs - crews, non-flying personnel, reservations equipment, communications, etc.

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They may have been "paid off" but until the cost of buying them is recovered, they're still and expense.

For example, I may have spent 6,000 on a car that I use for work, but until I've had that car make 6,000 for me(exclusive of operating costs), I still haven't "made money" on the car.  That's why you have depreciation.  The cost of obtaining the asset (car, airplane, piece of equipment) is depreciated over a period of time, as an operating expense, so that at the end of that period of time, it's "book value" is 0 dollars.  THAT's when any money made by that airplane starts being "clean" (exclusive of operating costs, etc.).

Oh fun topic, I took an entire class purely on the economics of the airline industry, very interesting stuff.  

Another thing to remember is that airlines these days aren't just buying aircraft, but a lot of them lease them.  Also, each aircraft has a pre-determined number of seats it can sell before it actually makes a profit.  And even though seats are inexpensive... multiply that by the number of occupied seats in the aircraft!  That's a lot of money being made!  Then multiply that by the number of that type of aircraft, average seats sold, and it can all add up really fast!  I mean, say an airplane sells an average of 100 seats a flight, at just $100 and the company puts out 10 flights a day in the aircraft, that's a good $100,000 a day or $700,000 a week or $3,000,000 a month.  Now subtract out several hundred thousand for maintenance and you can still make a bit of a profit.  

They have it down to an exact science to determine just exactally what price to make each seat, how many seats need to be sold to make the profit for every single aircraft and route.  

And as mentioned, scales of economy is a big thing, ie, how many of a product you need to sell before it makes a profit... it's one of the huge problems with aviation... for example it may take Boeing selling 40 747's before the company actually breaks even, but with Cessna it may take only 20 Caravans to break even.

Anyway, fun stuff, if you want me to bust out the charts, and "airline lingo" for ya, I'll do it.