Green’s Dictionary of Slang

to challenge someone to empty what remains of a bottle into their glass and then to drink it all down.

1785, 1788, 1796

Grose Classical Dict. of the Vulgar Tongue n.p.: to buzza one, is to challenge him to pour out all the wine in the bottle into his glass, undertaking to drink it, should it prove more than the glass would hold, it is commonly said to one who hesitates to empty a bottle that is nearly out.