"Master" is a term then often used for young boys in British society from those who serve them. "Mister", on the other hand, is generally used for adults. So basically, Heep is both making a snide insult against David by using a term for children, and also making reference to having known David since childhood.
The Schmoop study guide specifically mentions it being used in that context.
One last note on Uriah Heep: once Uriah meets up with David once more in London, when David is an apprentice proctor, you'll notice that he keeps confusing "Mister" and "Master" Copperfield. He claims that this confusion is accidental, because he has such affectionate memories of young Master Copperfield. Really, it's a power play: "Master" is a form of address for little boys, while Mister (obviously) is for grown men. Uriah Heep is trying to throw David off by reminding David how young he is, and that Uriah Heep has known him since he was a ragged little boy. Just another piece of psychological warfare from this master manipulator!