Kids ones you can bottom out easy as hell even in the correct weight ranges, so it's really nothing to worry about. If he's happy with them, leave it be I say. Also, it depends on his height, if he's under about 5'2" he'll struggle to use the adult stilts, even after modifying the footplate to be higher.
You're more likely to bottom out running than jumping as all your weight is on one spring, not shared between the two like when jumping.