Footing the bill?

The idiom foot the bill means basically

1. to pay all the costs for something.

2. pay the bill and settle the accounts. For ex. The bride's father was resigned to footing the bill for the wedding.

A "footing" is the foundation for something, or the "support." If you "foot" the bill for a project or anything else, then in a sense you're willing to support it, and pay it off.

Used in the set phrase foot up (to), meaning to count...“The united debts of the colony foot up something like £50,000"

"To foot a bill is attested from 1848, from the process of tallying the expenses and writing the figure at the bottom ("foot") of the bill."

I would suggest that you look up an interesting explanation for this expression given in the 'Source' below.

Walk this way.

Talk this way.

Take this away.

I am already gone.