I just recently sent some BTC from a wallet to cold storage, and it pulled the BTC from 3 different wallet address in order to get the amount I wanted to send.  The total transaction size showed 668 bytes, roughly 3 times the typical size.  Because of this, the fee I paid was over $4.

Is it normal that each wallet address that BTC is pulled from adds approx. 220 bytes to the transaction size?

I know that new wallet addresses are often generated for each deposit for privacy/security reasons, but from a fee standpoint wouldn't it cost a lot less to reuse a wallet address more than once?  This way, when money is sent from the wallet it's less likely to need to pull from so many addresses?