the regular "mature" sweetcorn is highly carby/calorific, meaning its treated as a starch along with the peas and parsnips. Its free on green/extra easy, but not super free.
Baby corn is very high in water, so low in calorie density, meaning it takes more to fill you up.
Sweet potatoes are much higher in sugar than normal potatoes, although they have a lower GI index, I don't know if that has something to do with why they are not a HEB.
Hope this helps.