Just a bit on the reel size, larger meaning longer casts, since spinning reels have the effect of line springing off of them, not being pulled off. A larger circumference would spring off more length of line as the line circles off the arbor.
If you overload a spinning reel, say fill it to the edge, you might add a bit of distance but you also dramatically increase the chances of a bird nest knot. I'd stay about a 1/8th or 1/16th inch back.
The really big determinants to casting light lures for your son will be the rod length and its elasticity; and, the line you choose to use.
A longer more elastic rod will sling a lure farther. St. Croix has some pretty long panfish rods that are built to cast well for ultralight.
And, Sufix has a new nanobraid with an impossibly small diameter that would shoot off the reel as good as any. You could still tie on a leader for your son depending on how you are fishing.
Sounds to me like you are obviously making casts for distance and not dropping a line off the side of a fishing dock.
Good luck! Brad