Green’s Dictionary of Slang

hip n.1

[SE, but note also hip, the n.]

(US Und.) a burden, a problem.

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[US]Jackson & Hellyer Vocab. Criminal Sl. 44: hip [...] A burden; an attachment; a responsibility; an incubus.

In phrases

get a bit on the hip (v.)

(Aus.) to have some money in reserve [one’s wallet is in the hip pocket].

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[Aus]Bulletin (Sydney) 13 May 40/2: You’re right now. Soon you get ‘a bit on the hip’ [...] fly back to unemployment, and get yourself ready to go through it all again.
on one’s hip

1. pressurising, harassing.

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[US]C. Mathewson Pitching in a Pinch 112: McGraw is always on Devore’s hip because he often feels that this brilliant young player does not get as much out of his natural ability as he might.

2. of a person, acting as a burden, a dependant.

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[US]Jackson & Hellyer Vocab. Criminal Sl. 44: I can’t see you tonight; I’ve got a Jane on my hip.
[UK](con. WW1) Hall & Niles One Man’s War 192: If those Britishers couldn’t be stopped before they dropped their bombs, we would have Switzerland on our hip.

3. having someone following one.

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[US]Jackson & Hellyer Vocab. Criminal Sl. 44: Don’t round, we’ve got somebody on our hip.