I don't want people to imagine me as having a massive belly or anything, but I've been consistently overweight for a few years now. There has been enough use of artificial sweeteners by millions if not billions of people that any serious health risk should have been obvious by now. If I drink artificially sweetened drinks and if this helps me lose weight, then I have may have an increased risk of some problems (illness or death) due to the artificial sweenteners, but these need to be balanced against descreased risk of illness or death if I'm no longer overweight or less overweight.
I've been eating and drinking less calories (artificially sweetened drinks are only part of this) for a few weeks, and one shirt that was a bit tight on me isn't so tight any more. I'll have to go weigh myself to see if this means that I've lost weight.
When I've dieted in the past and "fallen off the wagon", it's often been fizzy drinks which have been the tipping point. Hence while in a perfect world I might just substitute water or iced unsweetend tea of some form, I think it's reasonable to try diet soft drinks. I've got to the stage where Sainsbury's diet dry ginger ale isn't tasting too bad. But sweeter drinks such as their cream soda still taste pretty bad in their artificially sweetened form. Even though I do like the sweetened form.
BTW: I did do some research before I started drinking more artificial sweeteners. What I found didn't stop me drinking artificially sweetened drinks, but had the opposite effect of making me decide that it would be OK to drink drinks containing aspartame.