The tube doesn't make any difference at all. It's just a shaped rubber balloon that fills the available space within the tire and keeps the air from escaping.
In any case, while your son may be heavy for his afe or height, he's not at all heavy for 20" tires which have been used for adult folding bikes for ages, and can easily handle riders weighing well over 200#s.
If you don't have specific issues, don't fret. If you do have issues, they're more likely due to under inflation than anything else.
Otherwise, feel free to post your specific issue and somebody will offer sound advice.
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