This weekend, Burger King (BKW) will make its latest push to get fast-food eating Americans on its side with a two-day giveaway of the crinkled, lower-calorie Satisfries it recently started selling.

For the second-biggest burger chain measured by total locations, its ongoing fight for market share against competitors McDonald's (MCD) and Wendy's (WEN), as well as up-and-coming names like Smashburger and the fast-casual restaurants, will be partly influenced by how its fries measure up. With Satisfries, Burger King's hope is that what's being billed as healthier -- "40% less fat and 30% fewer calories" than McDonald's fries -- yet still tasting good, will do the trick.

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It's one of the latest examples of fast-food chains trying to appeal to a more health-conscious consumer. Stakes are high, and while the fry side of the eating-out market is big, with many, many players, it's also shrinking. Data from NPD Group show that, by number of servings, fries sales are down some 7% from the middle of 2007.

Bonnie Riggs, a restaurant industry analyst for the firm, says that U.S. consumers reported purchasing 10.8 billion servings of fries during the 12-month period from July 2012 to July 2013 -- more than 34 orders for every person living in the country. Of those, 8.7 billion were bought at fast-food shops. Fully 59% of the total, 6.4 billion servings, were at burger chains alone.

That's still below the 11.6 billion servings of just a few years ago, prior to the financial crisis. The downturn in fry sales was most noticeable during the recession, Riggs says, as diners looked for ways to cut costs. Another component of the decline resulted from a drop in sales of kids' meals. "Now having said that, in the last couple of years, it has leveled out, but it's flat. It's not growing," she says. "That's not a good thing for restaurant operators, because those french fries are a highly profitable item."

Burger King wants its cut. And it does get it. Though the Miami-based company's media relations department didn't respond to an emailed request for comment, Burger King said when it launched Satisfries that 50% of its customers ordered regular fries when they visited stores. The smallest version of the new fries are said to have 8 grams of fat and 190 calories, according to information Burger King has released. Its original fries start at 10 fat grams and 240 calories.

McDonald's, which has in excess of 14,000 U.S. units, roughly double Burger King's 7,200, is viewed as the market leader in fry sales. Bloomberg BusinessWeek reported last year that the Oak Brook, Ill., Big Mac maker sold 9 million lbs. of fries every day around the world. Riggs says NPD's policy is to not disclose specific company information. A McDonald's representative didn't reply to an emailed message to confirm the number.