In addition to testing rats, the study[1] compared five categories of drinks in humans: water, regular carbonated beverage (think soda), diet carbonated beverage (think diet soda), carbonated water and degassed regular carbonated beverage. They measured the release of ghrelin[2], the hormone which essentially tells your body you're hungry.
According to their results, both regular carbonated beverages, diet carbonated beverages and carbonated water resulted in noticeably increased amount of gherlin released (see [1] for the specifics).
So shortly put, it seems sparkling water makes you hungrier. That doesn't necessarily mean it will make you fat, giving in to the feeling of hunger is always up to you, but feeling more hungry sure as hell will make it likely that you will put on more weight.