We Never See Nothing

Let’s say for an example you deposit $1000 worth of bitcoin into an address and would like to pay a stranger on the internet to buy you a pizza. Naturally, you wouldn’t want to pay $1000 for a pizza so you transfer $20 worth of bitcoin to him. Doesn’t this meant that the public key corresponding to your address containing $980 worth of bitcoin has now been publicised and its security weakened?

I understand there must be a flaw in this reasoning but I can’t figure out what it is.

Thanks for any help.