This is not a complete answer but it won't fit well in a comment, and I'm hopeful that what I have to say will be somewhat helpful for you.
One of my children is at high genetic risk for diabetes. At some point some years back his weight kind of ballooned, he started feeling pretty lousy rather often (e.g. headaches, nausea, feeling like death warmed over), and he was diagnosed with pre-diabetes.
With the diagnosis, he was given a three-pronged treatment consisting of medication, moderate exercise e.g. walking for 30-40 minutes (as opposed to exercise in short spurts, such as sprints -- he's a really good sprinter), and a low-carb diet.
After two weeks of this treatment, his sugar cravings decreased dramatically, he started to lose weight (slowly), and he started to feel better.
After three months, he hit a plateau. Based on his body mass index (BMI) for age, he wasn't quite out of the obese region of the CDC chart yet. He was still complying well with the treatment, but his weight was steady for several weeks in a row.
I did some more reading about low-carb, and made two changes:
we substituted pizza sauce in place of catsup (because the pizza sauce was less sweet) (but note, we had never bought catsup with high-fructose corn syrup -- so that wasn't the issue)
we reduced the use of sugar-free gum (on the theory that the artificially sweetened gum was affecting him even though it didn't contain actual sugar)
These changes jump-started him and he went back to his slow weight loss. We found that when he got to the 85th percentile on the BMI for age chart, maintaining his weight at that level was pretty effortless, as long as he didn't get past about the 87th percentile. If his weight wandered up to the 90th percentile, it took some effort to get it back down. At the 85th, he felt much better and was able to have catsup and gum without his weight starting to balloon up.
Based on that experience, I think that an individual's tolerance of sweeteners depends on many factors. Also, I think that parent observations (and when your child is older, her own observations as well) can be quite helpful.
For our situation, it was helpful to eliminate refined grains, limit serving sizes of whole grains, and limit serving sizes of milk and fruit. We allowed unlimited amounts of protein and most vegetables, and included some form of protein in each meal and snack. Our kid was on board with the project. (He confided in his pediatrician that he wanted to look better in a bathing suit. Also, he wanted to feel better.)
A small addendum: before we got the diagnosis and treatment plan, many people assumed that we were feeding our child a lot of junk food, and/or we had created a lot of anxiety about food selection and amounts. If that ever happens to you, please don't let people's negative assumptions get to you.
Overall, I think the best way to gauge how much sweetener a child can handle may be by charting the child's BMI for age over the long term, and by being tuned in to how the child is feeling.
My personal opinion is that for most children who are at a non-worrisome weight, the only concern about sweetened foods I'd have is if the child is refusing to eat non-sweetened foods. Also I'd be concerned if the child refuses whole grain bread and brown rice, and insists on white bread and white rice. However, every family is different. Some families are vegan, some eat only raw foods, etc., and there's room for all of us on this earth.