I don't think you have to worry about offering her a sweet once a week. This is not going to make or break any weight issue she may have.

Keep in mind too that sometimes the baby pudge is greater in some children, and this will often linger into toddlerhood. My own son was VERY fat until he was about 20 months. He was in the 95th percentile for weight, and only 50th for height. All he ate was breast milk! He's 7 now, and is kind of on the wiry, slender side.

I would venture a guess that unless her parents are very obese, or unless this toddler has a health issue, the weight will come off now that she's active with your program, and the summer months are coming.