The disitinction between skinny and active - which is fine - and being skinny to the point of being listless - which is not - is the one you should be making. Kids who don't get enough food to be able to afford to run around fall short in their intellectual development. A few years ago Scientific American published the results of a South American study comparing the effects of various sorts of food supplements (protein-enriched did better).
Evidence? Caucasians can be fat as kids - as I was, and my brothers and couple of my cousins (not obese, just well-coverd). Japanese kids tended to be skinny because they used to be starved - the current generation is is pretty much up to Western height, which deals with the hereditary component there ...
My betting is that your weight distribution will have a long tail on the fat/obese side, and a shorp cut-off around skinny - very non-Gaussian.
Statistics? You've got a fair population suffering from "food insecurity" for whom your welfare system - such as it is -doesn't work.
What's really weird is that the richest country in the world has a significant proportion of its population suffering from food insecurity.
Your welfare system seems to be crippled for ideological reasons - you want to starve people back to work, even when there isn't any work to starve them back into. Your ideologues seems to be too stupid to realise that starving families damages them - and is particularly damaging to the kids, who are your next generation of workers.
In this context an effective welfare system fulfils the same function as the oil-soaked paper I wrap around my tools after I've used them. so that they will still be in good nick when I want to use them again.