In the experiments, rats who were fed artificially-sweetened foods tended to overeat foods containing real sweeteners, causing them to gain weight. In humans, it's the same result: drink diet soft drinks and consume enough foods made with artificial sweeteners, and you'll very likely overeat the sweets when the real thing comes along: apple pie, cookies, cake, ice cream, and so on.
This result is rather obvious, come to think of it: I don't recall ever seeing a thin person buying a twelve-pack of diet Pepsi at the grocery store. The people you see buying diet soft drinks are inevitably overweight or obese. Obviously, if diet soft drinks made people thin, you'd see lots of thin people buying them, right? It's common sense.
Further, all the thin people I know (including myself) wouldn't touch diet soft drinks, nor regular soft drinks. In fact, soft drinks are simply off the menu for anyone concerned with their health. They tend to be consumed by lower-income, lower-intelligence people who are more prone to advertiser influence and can't think for themselves.
But the real problem with artificial sweeteners today is their skyrocketing use in low-carb foods: Sucralose is used in practically every low-carb food bar, drink, snack, recipe or meal. And Sucralose very likely has the same effect as aspartame in this case: it trains your body to overconsume genuine refined carbohydrates when you encounter them.