Green’s Dictionary of Slang

1. to fall over when drunk.

c.1786		Grose Classical Dict. of the Vulgar Tongue ms. additions n.p.: Capsize to overturn or reverse. Sea term. He took his broth till he capsized.
1788, 1796		Grose Classical Dict. of the Vulgar Tongue n.p.: Capsize. To overturn or reverse. He took his broth till he capsized; he drank till he fell out of his chair.
1811		Lex. Balatronicum.
1818		M.L. Weems Drunkard’s Looking Glass (1929) 60: The drunkard’s looking glass, reflecting a faithful likeness of the drunkard, in sundry very interesting attitudes, [...] as first, when he has only ‘a drop in his eye;’ second, when he is ‘half shaved;’ third, when he is getting ‘a little on the staggers or so;’ and fourth, and fifth, and so on, till he is ‘quite capsized;’ or ‘snug under the table with the dogs,’ and can ‘stick to the floor without holding on.’.
1823		Egan Grose’s Classical Dict. of the Vulgar Tongue.

2. to overturn.

1785, 1788, 1796		see sense 1.
1811		see sense 1.
1823		‘Jon Bee’ Dict. of the Turf, the Ring, the Chase, etc. 21: Capsize — [...] to overturn any person or thing, any plan or resolution.
1900		Sporting Times 24 Mar. 1/2: As old Fogo, the veteran fob-diver, dashed up a blind alley off Drury Lane, he ran into and nearly capsized a more youthful get-a-bit.