There has been a lot of debate over the topic of artificial sweeteners and weight loss. Some studies say that artificial sweeteners do promote weight loss, while others argue the complete opposite, that artificial sweeteners cause weight gain.
Do artificial sweeteners in diet products affect weight loss?
Most diet products use artificial sweeteners because they provide the sweetness of sugar without adding any extra calories. How this affects weight loss is uncertain. Several studies, both long term and short term, favor each side of the debate.
A 1988 study1 had two groups of obese men and women. Both groups were placed on the same diet, except that one group had aspartame, an artificial sweetener used in some diet products, added to the diet. Both groups also had regular exercise instruction. The men in both groups lost a significant amount of weight in the 12 week period, while the women, who also had good results, had more of a difference in the two groups, with the group whose diet was supplemented with aspartame losing about four more pounds on average. This showed that artificial sweeteners can help weight loss, but because the group was small (59), no firm conclusions could be drawn.
Another similar study2 also showed positive results in taking aspartame. In a group of 163 obese women, some of them assigned to have products with aspartame and some assigned to abstain from it, it was shown that having aspartame promoted more weight loss and allowed more weight control during a follow-up period. This study had more conclusive evidence than the previous study, but still not enough to be considered definite.
One more study3 whose results leaned towards artificial sweeteners promoting weight loss (but still inconclusive) tested beverages with aspartame or high-fructose corn syrup (which I won't talk about because it's usually not used in diet products) on normal-weight men and women. The beverages with aspartame did appear, relative to when no beverages were given, to reduce weight in male subjects, but did not have a noticeable effect on females. Once again, this leaves us with an unsatisfactory result.
As I mentioned earlier, there are some studies that say artificial sweeteners don't have any significant effect on weight or sometimes even promote weight gain.
A long-term study in San Antonio4 studied a few thousand people and asked them how often they drank beverages with artificial sweeteners. The amount of total consumption of artificial sweeteners was then estimated. About 7 or 8 years later, the subjects were re-examined and it was found that higher consumption of artificial sweeteners may be linked with a higher body mass index (BMI) and weight gain. There are many other factors that could've changed this result, and they were handled as well as they could, but still not perfectly. Because of this, the result is once again inconclusive. The study article even says, "There may be no causal relationship between [artificial sweetener] use and weight gain."
One last study5 also says that there is no evidence that artificial sweetener consumption "helps weight loss or prevents weight gain." It showed no significant link between weight loss or gain and the amount of artificial sweeteners consumed. Of course, this study has many variables that were handled as adequately as possible, but still this leads to the real result of the experiment being inconclusive.
As we can see, it is nearly impossible to tell how artificial sweeteners affect weight loss. They're not really bad for your health, so it is fine to have them. It does seem that the studies that showed weight loss from artificial sweetener consumption had a higher percentage of weight difference than the studies that showed other results. From this you may conclude that the benefits outweigh the risks. The only thing I can recommend is to have artificial sweeteners in moderation, just like anything else.
Is there any benefit to choosing "diet" products instead over plain water?
This can also be a controversial subject, but there are also studies on it. Sadly, they are inconclusive.
This study6 tested men and women with two groups, one was an artificial sweetener beverage group and the other was a water group. Both groups also took part in a behavioral weight loss treatment program. The results showed that the artificial sweetener group lost more weight on average than the water group. Still, this study was not large enough and did not have sufficient enough evidence to be considered conclusive.
Whether diet products are better than water can still depend. You can argue the same as above that the benefits of artificial beverages outweigh the risks, but you could also say that water is a safe enough choice. This is usually up to whoever is debating between diet products and water, but your doctor can be contacted if the need is really felt.
 An evaluation of the effect of aspartame on weight loss.
 The effect of aspartame as part of a multidisciplinary weight-control program on short- and long-term control of body weight
 Effect of drinking soda sweetened with aspartame or high-fructose corn syrup on food intake and body weight
 Fueling the Obesity Epidemic? Artificially Sweetened Beverage Use and Long-term Weight Gain
 Artificial sweetener use and one-year weight change among women
 The effects of water and non-nutritive sweetened beverages on weight loss during a 12-week weight loss treatment program
Harvard - Artificial Sweeteners
Gain weight by “going diet?” Artificial sweeteners and the neurobiology of sugar cravings