So when you do a bitcoin transaction, you typically take a bunch of addresses, as inputs and you have one output. Due to this blend of addresses for input, I would argue (and many others have as well) that this makes a trail that is easy to trace back to many sources that would destroy your anonymity.
Now if each transaction only included one input and one output, and to pay someone you did a series of transactions, this would be extremely difficult to track, especially if the receiver gave you multiple addresses to send to.
So what would be the typical block byte overhead of doing multiple transactions (ignore fees):
addr_a -> addr_A
addr_b -> addr_B
addr_c -> addr_C
addr_c -> addr_D
the typical case of a single transaction:
( addr_a & addr_b & addr_c & addr_d )-> addr_A
(I am using upper case letters for receivers)