What does your hand do with a hat?

It can put it on and off, but you can do that with any part of your body... (that will reach the hat)

But what does a hand do to a hat that nothing else can.

It can TIP the hat.

And what can you do with your feet that has tip in it?

Tiptoe!

And it has to be FEET, not just foot... you can't tiptoe on one foot, as that would be toehopping.

The answer then, is

Hand is to hat as feet is to tip.

he has a top hat because he had a hand growing out of his head

hat

Hat