Full grown adults ride bikes (folding bikes, BMX) with 20" tires all the time. This has nothing to do with the weight of the rider. Other posters have already mentioned possible pinch flats which would result from under inflation of the tire. Keep in mind that tires lose air all the time and require frequently. If your son is not chcking his tire pressure at least weekly this could be your mainissue.
If you're getting repeated flats with the same tire try running your finger around the inside of the tire casing to find out if there is something sharp inside the tire. It works best if you can use a pair of thin cotton gloves to find the snag. I've found a number of surprising things inside my tire's carcasses including staples and thorns that can cause repeated flats if not removed.