The carcinogenic stuff is essentially BS.
The weight gain stuff is probably related to the fact that most popular artificial sweeteners will cause a spike in Insulin:
Thus, if you consume them together with a meal, they will essentially make your body more prone to:
a) Storing more of the glycogen (resulting from sugar) as fat, rather than inside the muscles
b) Make your want to eat more sugar or carbohydrates that can be easily broken down into sugar (Insulin has that effect, hormones play a few roles that go well together)
c) Stop your body from processing fat into energy, the mechanisms are a bit more complex here, the bottom line is, essentially, that insulin in the blood will signal to various glands and cells not to release the hormones and enzymes that allow your fat metabolism to kick into action.
However, the effect upon insulin release of most artificial sweeteners is mild. To top that off, protein can also trigger the release of insulin (see insulin index of various types of food if you want to read more into it). So there’s none saying that a protein based artificial sweeteners wouldn’t have the same effect… our endocrine systems are bloody complex.
