Metaphor: the ledger tips the scales

Greetings to all,

More than once, I've come upon a confusing metaphor dealing with the ledger, the scales of a balance, and tipping:

- George Seinfeld: All of the negative things about comedy that people say – how difficult it is, how humiliating it can be, comedy movies are never recognized, all that stuff – I erase all that, because I think the ledger still tips in our favor. (Gestures balance scales with his hands.)

- A business letter from Wisconsin: Employer's side of the ledger will tip the scales in the district's favor.

- A discussion board post: unceasing hard work, and a high voter turnout on the Republican side of the ledger will tip the scales. otherwise, we've got the Obama for his Second Term.

Now, I've checked that a 'ledger' can mean a business book of accounts, a wood strip used in scaffolding and formwork, a slab of stone laid over a grave, and a perforated ball of lead used in fishing. Only the first meaning seems to have any remote connection with scales. Here is some further explanation of the ledger: "In effect, the ledger is a classification and summarization of financial transactions and the basis for the preparation of the balance sheet and income statement. The ledger also allows one to see the balance in a given account at a particular time. For example, the cash balance at the end of the month can be seen to determine whether the business has a cash problem."

OK, entries in the ledger can change the account balance, sure. Maybe it can even be said that the ledger can tip the balance. But "scales"? The balance that scales are fitted to has nothing at all to do with an account balance. Is what we're dealing with here a case of a dead metaphor (or, perhaps, a mixed metaphor)? Are the speakers perhaps equating the two different balances; the account balance with the one that has scales?

I am waiting for your respected opinions,
Gus