What are the advantages, if any, by choosing weekly shipping over daily shipping?

If you win more than one auction a week then go with weekly, cost less. thats all.

Every week, Trish sends a tupperware box of her homemade 80-proof jigglers to one lucky weekly shipment client.

c/p from Cbid 'Help':

"Instead of paying individual shipping charges for each product, multiple items shipped to the same address won during the same shipping period (either DAILY or WEEKLY), only the greater of the shipping charges apply, plus $1 for each additional item ($0.50 for each additional item in 5-PACKS category; $0.25 for each additional item in the SINGLES category.)"

Weekly costs less, and saves trips to the mailbox.