monkey on (one's) back
A persistent burden or problem. Trust me, don't get in debt. You don't want that monkey on your back.
monkey on one's back
1. Drug addiction, as in He'd had a monkey on his back for at least two years. [Slang; first half of 1900s]
2. A vexing problem or burden, as in This project has proved to be a monkey on my back-there seems to be no end to it. Both usages allude to being unable to shake off the animal from one's back.
monkey on one's back
1. An addiction to a drug.
2. An object of persistent worry or obsession.