Green’s Dictionary of Slang

like sixty adv.

also sixty
[? SE like sixty men; on model of like twenty adv. and like forty adv.]

(orig. US) with great force or vigour, at a great speed.

[US]N.O. Picayune 8 Mar. 2/4: If they du come to hard blows the Maine boys ’ll flax out them are Brunswickers like sixty [DA].
[US]J.R. Lowell Biglow Papers (1880) 108: Like sixty all along I fumed an’ fussed an’ sorrered.
[US]C. Abbey diary 6 Dec. in Gosnell Before the Mast (1989) 242: We are nearly talked out Kanaka n. long for our letters ‘like sixty’.
[UK]Hotten Dict. of Modern Sl. etc.
[US]letter q. in Wiley Life of Billy Yank (1952) 333: He eats like sixty and does not have courage to stir to exercise it off.
[US]Appleton’s Journal (N.Y.) 9 Dec. 669: There is another class of similes scarcely as pertinent; as, for instance: [...] talk to him like a Dutch uncle; smiling as a basket of chips; odd as Dick’s hatband; happy as a clam at high water; quicker than you can say Jack Robinson; like all possessed; like fury; like all natur’; like all sixty; as quick as anything; mad as hops; mad as Halifax; sleep like a top; run like thunder; deader than a door-nail.
[US]J. Miller Memorie and Rime 22: Lizzie is a treasure, but she will lie like sixty.
[US]N.Y. Tribune 14 Feb. 16: He loves you like sixty.
[UK]A. Binstead Pitcher in Paradise 145: This cove is a-talkin to old Bob Moody, the Jockey Club janitor, like sixty.
[US]J. London Valley of the Moon (1914) 127: My eyes. They’re hurting like sixty.
[UK]L. Thomas Woodfill of the Regulars 30: He was just crampin’ and strugglin’ like sixty to stay on top.
[US](con. 1917–19) Dos Passos Nineteen Nineteen in USA (1966) 383: That Maine water was so cold that he came to like sixty.
[US]W. Guthrie Bound for Glory (1969) 139: I fired away like sixty.
[Aus]N. Pulliam I Travelled a Lonely Land (1957) 132: My host had told me a crew would ‘sometimes turn shy and shear like sixty’ when a woman entered the shed.
[US]‘Vin Packer’ Young and Violent 54: Down 102nd Street Junior Brown goes like sixty [...] He runs like crazy.
[US]S. King Stand (1990) 39: I woke up this morning sneezing and hacking away like sixty.
[US]‘Victoria Parker’ Pay for Play Cheerleaders [Internet] What man wouldn’t go like sixty on his prick if he had two beautiful young prick-teases urging him on?
E. Wood Back Home 67: Less wait till it gets all covered with ice, and all slick and smooth. [...] Say, won’t she go like sixty then!

In phrases

swing like sixty (v.) [swing v. (9a) ]

(US teen) to perform at one’s peak, to achieve ultimate success or pleasure.

[US]G. Sculatti Catalog of Cool [Internet] (to) swing like sixty (verb): To perform at peak, to freak freely or wail radically. ‘That girl’s the cleanest when it comes to threads. The dress she wore last night swung like sixty.’.
Songbirds Co-operative ‘Favourite Christmas Albums’ at MrLucky.com [Internet] Small wonder, then, that even the most timeworn Christmas numbers on this newly-released collection, like Sleigh Ride and Winter Wonderland, swing like sixty.
S. McElhaney ‘Groovy Threads’ at Hearsedriver.com [Internet] If ya can’t feel good, at least look good. These threads that swing like sixty!