If my child is getting back more on his state refund than he paid in, did I do something wrong? I've doublechecked the numbers. This doesn't make sense to me.

That makes no sense. Check AGAIN and look very very carefully for misplaced decimals and extra zeros or typos  in the amounts that were entered from his W-2 from boxes 16 and 17.   

I would delete the W2 and enter again manually.  That usually clears something out and fixes it.  Must have entered the state withholding in box 17  wrong.  What line on the state return seem wrong for payments?